Pasquale Calabrese and Andrea Gambassi 2005 J. Phys. A: Math. Gen. 38 R133 doi:10.1088/0305-4470/38/18/R01
Ageing properties of critical systems
REVIEW ARTICLEPasquale Calabrese1 and Andrea Gambassi2,3
Show affiliationsTOPICAL REVIEW
In the past few years, systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this everlasting non-equilibrium evolution. A simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high-temperature phase to the critical point. The aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case. Particular emphasis is put on the field-theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities. Fluctuation–dissipation relations are discussed and in particular the concept of fluctuation–dissipation ratio (FDR) is reviewed, emphasizing its connection with the definition of a possible effective temperature. The renormalization-group approach to critical dynamics is summarized and the scaling forms of the time-dependent non-equilibrium correlation and response functions of a generic observable are discussed. From them, the universality of the associated FDR follows as an amplitude ratio. It is then possible to provide predictions for ageing quantities in a variety of different models. In particular, the results for models A, B and C dynamics of the O(N) Ginzburg–Landau Hamiltonian, and model A dynamics of the weakly dilute Ising magnet and of the 
3 theory are reviewed and compared with the available numerical results and exact solutions. The effect of a planar surface on the ageing behaviour of model A dynamics is also addressed within the mean-field approximation.
- PACS
-
05.10.Cc Renormalization group methods
05.70.Jk Critical point phenomena
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
-
82B26 Phase transitions (general)
- Subjects
- Dates
-
Issue 18 (6 May 2005)
Received 11 October 2004, in final form 15 March 2005
Published 18 April 2005
-
Ageing properties of critical systems
Pasquale Calabrese and Andrea Gambassi 2005 J. Phys. A: Math. Gen. 38 R133
-
Scattering properties of ferroelectric domain walls
D A Bruce 1981 J. Phys. C: Solid State Phys. 14 5195
-
Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs
Peter Kuchment 2005 J. Phys. A: Math. Gen. 38 4887
-
The Environmental Dependence of the Fraction of ''Unconventional'' Galaxies: Red Late Types and Blue Early Types
Xin-Fa Deng et al. 2009 ApJ 699 948
-
The early days of the journal
J E Burns 2006 Phys. Med. Biol. 51 R1
-
Status of the joint LIGO–TAMA300 inspiral analysis
Stephen Fairhurst et al 2005 Class. Quantum Grav. 22 S1109
-
Accretion of Dust Grains as a Possible Origin of Metal-poor Stars with Low α/Fe Ratios
Toshikazu Shigeyama and Takuji Tsujimoto 2003 ApJ 598 L47
-
Random replicators with asymmetric couplings
Tobias Galla 2006 J. Phys. A: Math. Gen. 39 3853
-
Detection of Lead in the Carbon-rich, Very Metal-poor Star LP 625-44: A Strong Constraint on s-Process Nucleosynthesis at Low Metallicity
Wako Aoki et al 2000 ApJ 536 L97
-
How Do Uncertainties in the Surface Chemical Composition of the Sun Affect the Predicted Solar Neutrino Fluxes?
John N. Bahcall and Aldo M. Serenelli 2005 ApJ 626 530
Users also read
What's this?- Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
- Critical ageing of Ising ferromagnets relaxing from an ordered state
- Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Universality of Wigner random matrices: a survey of recent results