We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N gamma edges, with 1 < gamma <= 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 gamma at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter gamma, 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. (C) 2009 Elsevier B.V. All rights reserved.
Finite size effects for the Ising model on random graphs with varying dilution / Barre, J; Ciani, A; Fanelli, D; Bagnoli, F; Ruffo, S. - In: PHYSICA. A. - ISSN 0378-4371. - 388:(2009), pp. 3413-3425. [10.1016/j.physa.2009.04.024]
Finite size effects for the Ising model on random graphs with varying dilution
Ruffo, S
2009-01-01
Abstract
We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N gamma edges, with 1 < gamma <= 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 gamma at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter gamma, 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. (C) 2009 Elsevier B.V. All rights reserved.File | Dimensione | Formato | |
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