TY - JOUR
T1 - Mean-Field Theory is Exact for the Random-Field Model with Long-Range Interactions
AU - Tsuda, Junichi
AU - Nishimori, Hidetoshi
N1 - Publisher Copyright:
© 2014 The Physical Society of Japan We thank Dr. Takashi Mori for kind discussions.
PY - 2014/7/15
Y1 - 2014/7/15
N2 - 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.
AB - 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.
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U2 - 10.7566/JPSJ.83.074002
DO - 10.7566/JPSJ.83.074002
M3 - Article
AN - SCOPUS:84924872131
SN - 0031-9015
VL - 83
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
IS - 7
M1 - 074002
ER -