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

Author

Listed:
  • Barré, Julien
  • Ciani, Antonia
  • Fanelli, Duccio
  • Bagnoli, Franco
  • Ruffo, Stefano

Abstract

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

Suggested Citation

  • Barré, Julien & Ciani, Antonia & Fanelli, Duccio & Bagnoli, Franco & Ruffo, Stefano, 2009. "Finite size effects for the Ising model on random graphs with varying dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3413-3425.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:17:p:3413-3425
    DOI: 10.1016/j.physa.2009.04.024
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    Cited by:

    1. Serva, Maurizio, 2011. "Exact and approximate solutions for the dilute Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2443-2451.
    2. Serva, Maurizio, 2010. "Magnetization densities as replica parameters: The dilute ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2700-2707.

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