Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution

Details Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution

2009-02-03

arxiv.org/abs/0902.0564v1

Physics

Condensed Matter

Statistical Mechanics

21 pages, 6 figures, submitted to Physica A

Scientific paper

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 $1 < \gamma \leq 2$. 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.

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