Eur. Phys. J. B 47, 245-249 (2005)
https://doi.org/10.1140/epjb/e2005-00313-2

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

¹ Instituto de Física, Universidade de São Paulo, Caixa Postal 66318 05315-970, São Paulo, SP, Brazil
² Departamento de Física, Universidade Federal de Pernambuco, Recife, PE, Brazil

Corresponding authors: ^a mhase@if.usp.br - ^b almeida@df.ufpe.br - ^c ssalinas@if.usp.br

Received: 1 December 2004
Revised: 1 June 2005
Published online: 11 October 2005

Abstract

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field.