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Finite size effects for the Ising model on random graphs with varying dilution |
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| Authors: | Julien Barré Duccio Fanelli Franco Bagnoli Stefano Ruffo |
| Institution: | a Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice-Sophia Antipolis, Parc Valrose 06108 Nice, France b Dipartimento di Fisica, Università di Firenze, and INFN, Via Sansone 1, 50019 Sesto F.no (Firenze), Italy c Dipartimento di Energetica, Università di Firenze, and INFN, via S. Marta, 3, 50139 Firenze, Italy d CSDC, Centro interdipartimentale per lo Studio delle Dinamiche Complesse, Università di Firenze, Via Sansone 1, 50019 Sesto F.no (Firenze), Italy |
| 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. |
| Keywords: | 05 70 Fh 64 60 aq 64 60 an 75 10 Hk |
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