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

✍ Scribed by Julien Barré; Antonia Ciani; Duccio Fanelli; Franco Bagnoli; Stefano Ruffo

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 884 KB
• Volume: 388
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2009.04.024

✦ Synopsis

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N γ 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.