Finite size effects for the Ising model on random graphs with varying dilution

Julien Barré, Antonia Ciani, Duccio Fanelli, Franco Bagnoli and Stefano Ruffo

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 17, 3413-3425

Abstract: We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and Nγ edges, with 1<γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of γ at the transition temperature of the fully connected Curie–Weiss model. Finite size corrections are investigated for different values of the parameter γ, using two different approaches: a replica based finite N expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.

Keywords: Ising model; Random graphs; Finite size effects; Replica method; Cavity method (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:17:p:3413-3425

DOI: 10.1016/j.physa.2009.04.024

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