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
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.
PACS: 75.10.Nr – Spin-glass and other random models / 89.75.-k – Complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005