We study the classical spin model in random fields with long-range interactions and show the exactness of the meanfield theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spinglass cases. To treat random fields, we evoke the self-averaging property of a function of random fields, without recourse to the replica method. The result is that the mean-field theory gives the exact expression of the canonical free energy for systems with power-decaying interactions if the power is smaller than or equal to the spatial dimension.
ASJC Scopus subject areas
- Physics and Astronomy(all)