Table of contents

In this letter we investigate the effect of interfacial surfactant on the motion of an air bubble rising in a vertical capillary tube filled with a viscous fluid and sealed at one end. A thin layer of liquid, with almost constant thickness b, exists between the bubble interface and the tube wall. The fluid displaced by the front meniscus flows down through this layer because the tube is sealed far up at the top. The steady rising velocity U of the bubble is related to the thickness b. An upper bound for U is obtained in terms of b and other physical data of the problem, which is in good agreement with previous experimental results. It is proved here analytically that the presence of surfactant on the bubble interface causes a thinning and a delay effect: the thickness of the liquid layer behind the bubble and the rise velocity of the bubble are smaller than those for the 'clean' case. Exactly the opposite effect of surfactant in the horizontal case has been derived analytically by Daripa and Pasa (2010 J. Stat. Mech. L02002) and numerically by Ratulowski and Chang (1990 J. Fluid Mech.210 303). These effects of interfacial surfactant are consistent with previous experimental and numerical results.

We study an extension of the voter model in which each agent is endowed with an innate preference for one of two states that we term as 'truth' or 'falsehood'. Due to interactions with neighbors, an agent that innately prefers truth can be persuaded to adopt a false opinion (and thus be discordant with its innate preference) or the agent can possess an internally concordant 'true' opinion. Parallel states exist for agents that inherently prefer falsehood. We determine the conditions under which a population of such agents can ultimately reach a consensus for the truth, reach a consensus for falsehood, or reach an impasse where an agent tends to adopt the opinion that is in internal concordance with its innate preference with the outcome that consensus is never achieved.

We consider dissipative dynamical systems represented by a smooth compressible flow in a finite domain. The density evolves according to the continuity (Liouville) equation. For a general, non-degenerate flow the result of the infinite time evolution of an initially smooth density is a singular measure. We give a condition for the non-degeneracy which allows us to decide for a given flow whether the infinite time limit is singular. The condition uses a Green–Kubo-type formula for the space-averaged sum of forward- and backward-in-time Lyapunov exponents. We discuss how the sums determine the fluctuations of the entropy production rate in the SRB state and give examples of computation of the sums for certain velocity fields.

We study the fractal properties of interfaces in the 2d Ashkin–Teller model. The fractal dimension of the symmetric interfaces is calculated along the critical line of the model in the interval between the Ising and the four-states Potts models. Using Schramm's formula for crossing probabilities we show that such interfaces cannot be related to the simple SLE_κ, except for the Ising point. The same calculation on non-symmetric interfaces is performed in the four-states Potts model: the fractal dimension is compatible with the result coming from Schramm's formula, and we expect a simple SLE_κ in this case.

We characterize the influence of the presence of suspended particles on a fluid undergoing convection and find that it leads to deviations in both the fluid speed and temperature. The spatio-temporal deviations of the profiles for both fields are persistent in several well-defined regions of the fluid. We find these variations to be robust and to be exhibited by different temperature profiles, although the strength of the deviations depends on the amount of time required by the suspension to reach a steady state. The primary effect of the presence of the particles is to weaken the fluid convective strength and heat flux, as well as to change the convection's spatial characteristics. The results quantify the degree to which the physical presence and motion of particles in a suspension affect its flow dynamics, a case that is typically neglected in most modeling protocols.

We consider spin-polarized Abelian quantum Hall states in the Tao–Thouless limit, i.e. on a thin torus. For any filling factor ν = p/q a well-defined sector of low energy states is identified and the exclusion statistics of the excitations is determined. We study numerically, at and near ν = 1/3 and 2/5, how the low energy states develop as one moves away from the Tao–Thouless limit towards the physical regime. We find that the lowest energy states in the physical regime develop from states in the low energy sector but that the exclusion statistics is modified.

Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of the control parameter in a finite system. In this paper, we study what kind of transition takes place in finite systems of nonequilibrium wetting models. By solving exactly a microscopic model with three and four sites and performing numerical simulations we show that the phase transition taking place in a finite system is characterized by the average interface height performing a random walk at criticality and does not discriminate between the bounded-KPZ classes and the bounded-EW class. We also study the finite size scaling of the bKPZ universality classes, showing that it presents peculiar features in comparison with other universality classes of nonequilibrium phase transitions.

In a recent study (Miller and Shnerb 2010 arXiv:1011.3254) the contact process with a modified creation rate at a single site was shown to exhibit a non-universal scaling behavior with exponents varying with the creation rate at the special site. In the present work we argue that the survival probability decays according to a stretched exponential rather than a power law, explaining previous observations.

We consider an asymmetric variant of disordered Glauber dynamics of Ising spins on a one-dimensional lattice, where each spin flips according to the relative state of the spin to its left. Moreover, each bond allows for two rates: flips which equalize nearest neighbour spins, and flips which 'unequalize' them. In addition, the leftmost spin flips depending on the spin at that site. We explicitly calculate all eigenvalues of the transition matrix for all system sizes and conjecture a formula for the normalization factor of the model. We then analyse two limits of this model, which are analogous to ferromagnetic and antiferromagnetic behaviour in the Ising model, for which we are able to prove an analogous formula for the normalization factor.

We construct a transport model for particles that alternate rests of random duration and flights with random velocities. The model provides a balance equation for the mesoscopic particle density obtained from the continuous-time random walk framework. By assuming power laws for the distributions of waiting times and flight durations (for any velocity distribution with finite moments) we have found that the model can yield all the transport regimes ranging from subdiffusion to ballistic depending on the values of the characteristic exponents of the distributions. In addition, if the exponents satisfy a simple relationship it is shown how the competition between the tails of the distributions gives rise to a diffusive transport. Finally, we explore how the details of this intermittent transport process affect the success probability in an optimal search problem where an individual searcher looks for a target distributed (heterogeneously) in space. All the results are conveniently checked with numerical simulations.

We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii–Kosterlitz–Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation length and the density of topological defects (vortices). By using Monte Carlo simulations we first determine the time and temperature dependence of the growing correlation length after an infinitely rapid quench from above the transition temperature to the quasi-long-range order region. The functional form is consistent with a logarithmic correction to the diffusive law and it serves to validate dynamic scaling in this problem. This analysis clarifies the different dynamic roles played by bound and free vortices. We then revisit the Kibble–Zurek mechanism in thermal phase transitions in which the disordered state is plagued with topological defects. We provide a theory of quenching rate dependence in systems with the BKT-type transition that goes beyond the equilibrium scaling arguments. Finally, we discuss the implications of our results for a host of physical systems with vortex excitations, including planar ferromagnets and liquid crystals.

We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some special energies. We provide a consistent picture for two well-known one-dimensional examples: the chain with off-diagonal disorder and the random-dimer model. In both cases the quantum motion exhibits a peculiar kind of anomalous diffusion which can be referred to as bi-fractality. The disorder-averaged density profile of the particle becomes critical in the long-time regime. The qth moment of the position of the particle diverges with time whenever  q exceeds some q₀. We obtain q₀ = 2 for off-diagonal disorder on the chain (and conjecturally on two-dimensional bipartite lattices as well). For the random-dimer model, our result q₀ = 1/2 corroborates known rigorous results.

The one-dimensional coagulation–diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain, such that one of them disappears with probability one if two particles meet. The exact two-time correlation and response functions in the one-dimensional coagulation–diffusion process are derived from a generalization of the empty-interval method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the long-time ageing regime. A new generalized fluctuation-dissipation ratio with a universal and finite limit is proposed.

We study a model of self-propelled particles exhibiting run-and-tumble dynamics on a lattice. This non-Brownian diffusion is characterized by a random walk with a finite persistence length between changes of direction and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particles and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run-and-tumble dynamics. We solve the externally driven non-interacting and zero-range versions of the model exactly and utilize a field-theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to run-and-tumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes an efficient tool to simulate a class of interacting run-and-tumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met.

Using some modification of the standard fermion technique we derive factorized formulas for spin operator matrix elements (form factors) between general eigenstates of the Hamiltonian of the quantum Ising chain in a transverse field of finite length. The derivation is based on the approach recently used to derive factorized formulas for Z_N-spin operator matrix elements between ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable chiral Potts quantum chain. The obtained factorized formulas for the matrix elements of the Ising chain coincide with the corresponding expressions obtained by the separation of variables method.

Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links.

Here we propose a simple shift in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori.

The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved.

We explore the noise-induced barrier crossing dynamics of a Brownian particle in the high temperature quantum regime under large damping. We assume the associated heat bath not to be in thermal equilibrium; it is rather driven by an externally applied random force which exposes the system particles to a nonequilibrium environment. We propose a system + reservoir model to study the stochastic Langevin dynamics. We also construct the corresponding Fokker–Planck equation in the said regime and solve it to explore the bistable kinetics. We investigate the role of different parameters in shaping the nature of such a bistable kinetics in detail and hence allowing one to get some insight into the very complicated dynamics of quantum dissipative system(s). Finally, we analyze the semiclassical rate vis-à-vis the classical analog.

In this paper, we investigate the complex dynamics of a reaction–diffusion I–R model with a nonlinear rate of incidence of saturated mass action under zero-flux boundary conditions. We give an analysis of the boundedness, dissipation, and local and global stability of the positive equilibria. And we show the conditions for Turing instability and determine the Turing space in the parameter space. On the basis of these results, we present the evolutionary processes that involve organism distribution and the interaction of spatially distributed infection with local diffusion, and we find that the model dynamics exhibits a diffusion-controlled formation growth of spot, stripe–spot, stripe, stripe–hole and hole pattern replication. Furthermore, we indicate that the speed of disease spreading increases with the parameter A or the diffusion of infection increasing.

We investigate by means of numerical simulation the system-size dependence of the shear delamination strength of thin elastic films. The films are connected to a rigid substrate by a disordered interface containing a pre-existing crack. The size dependence of the strength of this system is found to depend crucially on the crack shape. For circular cracks, we observe a crossover between a size-independent regime at large crack radii which is controlled by propagation of the pre-existing crack, and a size-dependent regime at small radii which is dominated by nucleation of new cracks in other locations. For cracks of finite width that span the system transversely, we observe for all values of the crack length a logarithmic system-size dependence of the failure stress. The results are interpreted in terms of extreme value statistics.

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated with models fulfilling the proposed criteria.

We investigate the diffusion equation subjected to the boundary conditions and , and the initial condition . We obtain exact solutions in terms of the Green function approach and analyze the mean square displacement in the x and y directions. This analysis shows an anomalous spreading of the system which is characterized by different diffusive regimes connected to anomalous diffusion.

We consider the critical spin–spin correlation function of the 2D Ising model with a line defect whose strength is an arbitrary function of the position. By using path integral techniques in the continuum description of this model in terms of fermion fields, we obtain an analytical expression for the correlator as a functional of the position-dependent coupling. Thus, our result provides one of the few analytical examples that allows one to illustrate the transit of a magnetic system from scaling to non-scaling behavior in a critical regime. We also show that the non-scaling behavior obtained for the spin correlator along a nonuniformly altered line of an Ising model remains unchanged in the Ashkin–Teller model.

We investigate by means of Monte Carlo simulations the zipping and unzipping dynamics of two polymers connected at one end and subject to an attractive interaction between complementary monomers. In zipping, the polymers are quenched from a high temperature equilibrium configuration to a low temperature state, such that the two strands zip up by closing up a 'Y'-fork. In unzipping, the polymers are brought from a low temperature double-stranded configuration to high temperatures, such that the two strands separate. Simulations show that the unzipping time, τ_u, scales as a function of the polymer length as τ_u ∼ L, while the zipping is characterized by the anomalous dynamics τ_z ∼ L^α with α = 1.37(2). This exponent is in good agreement with simulation results and theoretical predictions for the scaling of the translocation time of a forced polymer passing through a narrow pore. We find that the exponent α is robust against variations of parameters and temperature, whereas the scaling of τ_z as a function of the driving force shows the existence of two different regimes: the weak forcing (τ_z ∼ 1/F) and strong forcing (τ_z independent of F) regimes. The crossover region is possibly characterized by a non-trivial scaling in F, matching the prediction of recent theories of polymer translocation. Although the geometrical setups are different, zipping and translocation share thus the same type of anomalous dynamics. Systems where this dynamics could be experimentally investigated include DNA (or RNA) hairpins: our results imply an anomalous dynamics for the hairpins' closing times, but not for the opening times.

Message-passing algorithms based on belief propagation (BP) are implemented on a random constraint satisfaction problem (CSP) referred to as model RB, which is a prototype of hard random CSPs with growing domain size. In model RB, the number of candidate discrete values (the domain size) of each variable increases polynomially with the variable number N of the problem formula. Although the satisfiability threshold of model RB is exactly known, finding solutions for a single problem formula is quite challenging and attempts have been limited to cases of N ∼ 10². In this paper, we propose two different kinds of message-passing algorithms guided by BP for this problem. Numerical simulations demonstrate that these algorithms allow us to find a solution for random formulas of model RB with constraint tightness slightly less than p_cr, the threshold value for the satisfiability phase transition. To evaluate the performance of these algorithms, we also provide a local search algorithm (random walk) as a comparison. Besides this, the simulated time dependence of the problem size N and the entropy of the variables for growing domain size are discussed.

We consider a non-equilibrium three-state model whose dynamics is Markovian and displays the same symmetry as the three-state Potts model, i.e. the transition rates are invariant under the cyclic permutation of the states. Unlike the Potts model, detailed balance is, in general, not satisfied. The aging and the stationary properties of the model defined on a square lattice are obtained by means of large-scale Monte Carlo simulations. We show that the phase diagram presents a critical line, belonging to the three-state Potts universality class, that ends at a point whose universality class is that of the Voter model. Aging is considered on the critical line, at the Voter point and in the ferromagnetic phase.

Networks commonly exhibit a community structure, whereby groups of vertices are more densely connected to each other than to other vertices. Often these communities overlap, such that each vertex may occur in more than one community. However, two distinct types of overlapping are possible: crisp (where each vertex belongs fully to each community of which it is a member) and fuzzy (where each vertex belongs to each community to a different extent). We investigate the effects of the fuzziness of community overlap. We find that it has a strong effect on the performance of community detection methods: some algorithms perform better with fuzzy overlapping while others favour crisp overlapping. We also evaluate the performance of some algorithms that recover the belonging coefficients when the overlap is fuzzy. Finally, we investigate whether real networks contain fuzzy or crisp overlapping.

The goal of this work is a comparative study of two Wright–Fisher-like diffusion processes on the interval, one due to Karlin and the other one due to Kimura. Each model accounts for the evolution of one two-locus colony undergoing random mating, under the additional action of selection in a random environment. In other words, we study the effect of disorder on the usual Wright–Fisher model with fixed (nonrandom) selection. There is a drastic qualitative difference between the two models and between the random and nonrandom selection hypotheses.

We first present a series of elementary stochastic models and tools that are needed to conduct this study in the context of diffusion process theory, including Kolmogorov backward and forward equations, scale and speed functions, classification of boundaries, and Doob transformation of sample paths using additive functionals. In this spirit, we briefly revisit the neutral Wright–Fisher diffusion and the Wright–Fisher diffusion with nonrandom selection.

With these tools at hand, we first deal with the Karlin approach to the Wright–Fisher diffusion model with randomized selection differentials. The specificity of this model is that in the large population case, the boundaries of the state space are natural and hence inaccessible, and so quasi-absorbing only. We supply some limiting properties pertaining to times of hitting of points close to the boundaries.

Next, we study the Kimura approach to the Wright–Fisher model with randomized selection, which may be viewed as a modification of the Karlin model, using an appropriate Doob transform which we describe. This model also has natural boundaries, but they turn out to be much more attracting and sticky than in Karlin's version. This leads to a faster approach to the quasi-absorbing states, to a larger time needed to move from the vicinity of one boundary to the other and to a local critical behavior of the branching diffusion obtained after the relevant Doob transformation.

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.

We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale-free property of the perturbative expansions, we find exact expressions for the order parameters, yielding the critical exponents. We show that the ground state of this fermion chain and another model in the same universality class, the XYZ chain along a line of couplings, are both written in terms of the same polynomials. We demonstrate this explicitly for up to N = 24 sites and provide consistency checks for large N. These polynomials satisfy a recursion relation related to the Painlevé VI differential equation and, using a scale-free property of these polynomials, we derive a simple and exact formula for their limit.

We show that the partition function of many classical models with continuous degrees of freedom, e.g. Abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four-dimensional lattice gauge theory (LGT) with gauge group U(1). This result is very general in that it includes models in different dimensions with different symmetries. In particular, we show that a U(1) LGT defined in a curved spacetime can be mapped to a U(1) LGT with a flat background metric. The result is achieved by expressing the U(1) LGT partition function as an inner product between two quantum states.

We present a generalization of Gibbs statistical mechanics designed to describe a general class of stationary and metastable equilibrium states. It is assumed that the physical system maximizes the entropy functional S subject to the standard conditions plus an extra conserved constraint function F, imposed to force the system to remain in the metastable configuration. After requiring additivity for two quasi-independent subsystems, and the commutation of the new constraint with the density matrix ρ, it is argued that F should be a homogeneous function of ρ, at least for systems in which the spectrum is sufficiently dense to be considered as continuous. Therefore, surprisingly, the analytic form of F turns out to be of the kind F(p_i) = p_i^q, where the p_i are the eigenvalues of the density matrix and q is a real number to be determined. Thus, the discussion identifies the physical relevance of Lagrange multiplier constraints of the Tsallis kind and their q parameter, as enforced by the additivity of the constraint F which fixes the metastable state. An approximate analytic solution for the probability density is found for q close to unity. The procedure is applied to describe the results from the plasma experiment of Huang and Driscoll. For small and medium values of the radial distance, the measured density is predicted with a precision similar to that achieved by minimal enstrophy and Tsallis procedures. Also, the particle density is predicted at all the radial positions. Thus, the discussion gives a solution to the conceptual difficulties of the two above mentioned approaches as applied to this problem, which both predict a non-analytic abrupt vanishing of the density above a critical radial distance.

The cracking, shearing and stick–slip motions in sea ice are similar to those in fracturing geostructures. In this work, the fracture-related, quasi-seismic activity in the Arctic ice pack was monitored during a large-scale ice cover fragmentation that occurred in March 2008. This fragmentation resulted in the formation of a two-dimensional 'fault' clearly seen in satellite images. The energy distribution in elastic waves detected by seismic tiltmeters follows the power law in pre- and post-faulting periods. The power exponent decreases as the 'catastrophe' approaches, and exhibits a trend to restore its initial value after the large-scale perturbation. The detected fracture events are correlated in time in the sense of a scaling relation. A quiescent period (very low quasi-seismic activity) was observed before 'faulting'. A close similarity in scaling characteristics between the crustal seismicity and quasi-seismic activity observed in the ice pack is discussed from the viewpoint of the role of heterogeneity in the behavior of large-scale critical systems.

It is well known that increase of the spatial dimensionality enhances the fluid–fluid demixing of a binary mixture of hard hyperspheres, i.e. the demixing occurs for lower mixture size asymmetry as compared to the three-dimensional case. However, according to simulations, in the latter dimension the fluid–fluid demixing is metastable with respect to the fluid–solid transition. According to the results obtained from approximations to the equation of state of hard hyperspheres in higher dimensions, the fluid–fluid demixing might become stable for high enough dimension. However, this conclusion is rather speculative since none of these works have taken into account the stability of the crystalline phase (by a minimization of a given density functional, by spinodal calculations or by MC simulations). Of course, the lack of results is justified by the difficulty of performing density functional calculations or simulations in high dimensions and, in particular, for highly asymmetric binary mixtures. In the present work, we will take advantage of a well tested theoretical tool, namely the fundamental measure density functional theory for parallel hard hypercubes (in the continuum and in the hypercubic lattice). With this, we have calculated the fluid–fluid and fluid–solid spinodals for different spatial dimensions. We have obtained, no matter what the dimensionality, the mixture size asymmetry or the polydispersity (included as a bimodal distribution function centered around the asymmetric edge lengths), that the fluid–fluid critical point is always located above the fluid–solid spinodal. In conclusion, these results point to the existence of demixing between at least one solid phase rich in large particles and one fluid phase rich in small ones, preempting a fluid–fluid demixing, independently of the spatial dimension or the polydispersity.

We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range character of correlations is translated into a broad distribution of the spin–spin correlation coefficients for almost all realizations of the random couplings. When we sample the whole phase space we find that this distribution is indeed so broad that at low temperatures it essentially becomes uniform, with all possible correlation values appearing with the same probability. The distribution of correlations inside a single phase space valley is also studied and found to be much narrower.

We investigate the corrections to scaling of the Rényi entropies of a region of size at the end of a semi-infinite one-dimensional system described by a conformal field theory when the corrections come from irrelevant boundary operators. The corrections from irrelevant bulk operators with scaling dimension x have been studied by Cardy and Calabrese (2010), and they found not only the expected corrections of the form but also unusual corrections that could not have been anticipated from standard finite-size scaling. However, for the case of perturbations from irrelevant boundary operators we find that the only corrections that can occur to leading order are of the form for boundary operators with scaling dimension x_b < 3/2, and when x_b > 3/2. When x_b = 3/2 they are of the form . A marginally irrelevant boundary perturbation will give leading corrections going as . No unusual corrections occur when perturbing with a boundary operator.

In this paper we report a theoretical model based on Green's functions and averaging techniques that describes the dynamics of parametrically driven mechanical resonators under the action of thermal noise. Quantitative estimates for cooling, heating, and quadrature thermal noise squeezing near the first parametric instability zone of the oscillator are given. Furthermore, the parameter space where these phenomena occur is presented. Very good agreement between analytical estimates and numerical results is achieved.

We propose a theoretical framework to analyze nuclear magnetic resonance (NMR) experiments for the description of dispersion processes featuring memory effects. Memory effects, addressed here, can be represented by subordinated Brownian motions with random time changes that invert Lévy time processes, with stable densities of exponent between 0 and 1. According to whether the Lévy process has a drift equal to zero or not, the subordinated motion has a p.d.f that solves the fractional Fokker–Planck equation or the fractal mobile/immobile model. NMR experiments can measure the characteristic function of displacements of water molecules and facilitate their interpretation in media showing memory effects. We give mathematical expressions for the moments and averaged exponentials of the increment of subordinated Brownian motions within the framework of fractal MIM and FFPE. The results are illustrated on the basis of a numerical method.

Large-scale data resulting from users' online interactions provide the ultimate source of information to study emergent social phenomena on the Web. From individual actions of users to observable collective behaviors, different mechanisms involving emotions expressed in the posted text play a role. Here we combine approaches of statistical physics with machine-learning methods of text analysis to study the emergence of emotional behavior among Web users. Mapping the high-resolution data from digg.com onto bipartite networks of users and their comments onto posted stories, we identify user communities centered around certain popular posts and determine emotional contents of the related comments by the emotion classifier developed for this type of text. Applied over different time periods, this framework reveals strong correlations between the excess of negative emotions and the evolution of communities. We observe avalanches of emotional comments exhibiting significant self-organized critical behavior and temporal correlations. To explore the robustness of these critical states, we design a network-automaton model on realistic network connections and several control parameters, which can be inferred from the dataset. Dissemination of emotions by a small fraction of very active users appears to critically tune the collective states.

We study the effects of disorder on the slope of the disorder–temperature phase boundary near the Onsager point (T_c = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques, we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.

The recently introduced multifractal network generator (MFNG), has been shown to provide a simple and flexible tool for creating random graphs with very diverse features. The MFNG is based on multifractal measures embedded in 2d, leading also to isolated nodes, whose number is relatively low for realistic cases, but may become dominant in the limiting case of infinitely large network sizes. Here we discuss the relation between this effect and the information dimension for the 1d projection of the link probability measure (LPM), and argue that the node isolation can be avoided by a simple transformation of the LPM based on rotation.

We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards–Anderson spin glass model with bimodal couplings (J = ± 1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and low enough link density), where spins are long range correlated, even if the ground state energy stiffness is null. In other words, in this region twisting the boundary conditions costs no energy, but spins are long range correlated by means of pure entropic effects.

In this paper we develop a new approach to the investigation of the bi-partite entanglement entropy in integrable quantum spin chains. Our method employs the well-known replica trick, thus taking a replica version of the spin chain model as starting point. At each site i of this new model we construct an operator which acts as a cyclic permutation among the n replicas of the model. Infinite products of give rise to local operators, precursors of branch-point twist fields of quantum field theory. The entanglement entropy is then expressed in terms of correlation functions of such operators. Employing this approach we investigate the von Neumann and Rényi entropies of a particularly interesting quantum state occurring as a limit (in a compact convergence topology) of the antiferromagnetic XXZ quantum spin chain. We find that, for large sizes, the entropy scales logarithmically, but not conformally.