Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
Disordered Systems and Neural Networks
2009-11-10 v4
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.
Cite
@article{arxiv.cond-mat/0411682,
title = {Replica-symmetric solutions of a dilute Ising ferromagnet in a random field},
author = {M. O. Hase and J. R. L. de Almeida and S. R. Salinas},
journal= {arXiv preprint arXiv:cond-mat/0411682},
year = {2009}
}