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

Junichi Tsuda, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number7
Publication statusPublished - 2014 Jul 15

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Mean-Field Theory is Exact for the Random-Field Model with Long-Range Interactions'. Together they form a unique fingerprint.

Cite this