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

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 $1<\gamma \le 2$. 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.

21 pages, 6 figures, submitted to Physica A

References in corpus (6)

• Critical phenomena in complex networks
• The mean field Ising model trough interpolating techniques
• Criticality in diluted ferromagnet
• Mean field dilute ferromagnet I. High temperature and zero temperature behavior
• Exact and Approximate Solutions for the Dilute Ising Model
• Magnetization Densities as Replica Parameters: The Dilute Ferromagnet

Cited by in corpus (6)

• Exact and Approximate Solutions for the Dilute Ising Model
• A Two-populations Ising model on diluted Random Graphs
• Magnetization Densities as Replica Parameters: The Dilute Ferromagnet
• Stochastic Bifurcations in the Nonlinear Parallel Ising Model
• Ensemble inequivalence and absence of quasi-stationary states in long-range random networks
• Free energy equivalence between mean-field models and nonsparsely diluted mean-field models