Andrea Montanari and Antoine Sinton J. Stat. Mech. (2007) P08004 doi:10.1088/1742-5468/2007/08/P08004
Andrea Montanari1 and Antoine Sinton2
Show affiliationsWe define a new family of random spin models with one-dimensional structure, finite-range multispin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be described as solutions of a sparse, band diagonal linear system, thus allowing for efficient numerical analysis.
In the limit of infinite interaction range, we recover the so-called XORSAT (diluted p-spin) model that is known to undergo a random first-order phase transition as the average degree is increased. Here we investigate the most important consequences of a large but finite interaction range: (i) fluctuation-induced corrections to thermodynamic quantities; (ii) the need of an inhomogeneous (position-dependent) order parameter; (iii) the emergence of a finite mosaic length scale. In particular, we study the correlation length divergence at the (mean field) glass transition.
E-print Number: 0705.0054
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Refers: to
75.10.Nr Spin-glass and other random models
64.70.P- Glass transitions of specific systems
65.60.+a Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.
82C26 Dynamic and nonequilibrium phase transitions (general)
82C44 Dynamics of disordered systems (random Ising systems, etc.)
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
Issue 08 (August 2007)
Received 7 May 2007, accepted for publication 11 June 2007
Published 1 August 2007
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