# Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution - Condensed Matter > Statistical Mechanics

Abstract: We investigate the finite size corrections to the equilibrium magnetizationof 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 freeenergy is made extensive. As expected, the system displays a phase transitionof the mean-field type for all the considered values of $\gamma$ at thetransition temperature of the fully connected Curie-Weiss model. Finite sizecorrections are investigated for different values of the parameter $\gamma$,using two different approaches: a replica-based finite $N$ expansion, and acavity method. Numerical simulations are compared with theoretical predictions.The cavity based analysis is shown to agree better with numerics.

Author: Julien Barre', Antonia Ciani, Duccio Fanelli, Franco Bagnoli, Stefano Ruffo

Source: https://arxiv.org/