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.
2009
388
3413
3425
http://www.sciencedirect.com/science/article/pii/S037843710900329X
https://arxiv.org/abs/0902.0564
Barre, J; Ciani, A; Fanelli, D; Bagnoli, F; Ruffo, S
File in questo prodotto:
File Dimensione Formato  
BarreCianiFanelliBagnoliRuffo-FiniteSizeEffectsIsing-PhyscaA388-3413.pdf

non disponibili

Licenza: Non specificato
Dimensione 883.94 kB
Formato Adobe PDF
883.94 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11564
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 7
social impact