Mean-Field Theory is Exact for the Random-Field Model with Long-Range Interactions

Junichi Tsuda, Hidetoshi Nishimori

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number074002
Journaljournal of the physical society of japan
Volume83
Issue number7
DOIs
Publication statusPublished - 2014 Jul 15
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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