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arXiv · 1402.1581

Mean-field theory is exact for the random-field model with long-range interactions

Junichi Tsuda·Hidetoshi Nishimori
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Abstract

We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass 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.

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Junichi Tsuda, Hidetoshi Nishimori. 2014-02-07. Mean-field theory is exact for the random-field model with long-range interactions. https://doi.org/10.7566/jpsj.83.074002

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