The short-range van Hemmen model in a simple Kikuchi approximation: Comparison with the mean-field model and with spin-glasses

Ph. De Smedt, J.O. Indekeu and L. Zhang

Physica A: Statistical Mechanics and its Applications, 1987, vol. 140, issue 3, 450-477

Abstract: A simple first-order Kikuchi approximation is studied for the short-range (nearest-neighbour) version of the van Hemmen mean-field model originally proposed for spin-glasses. Although the approximation is very similar to the mean-field treatment, the phase diagrams from the two methods are drastically different. Previously reported results are reviewed and extended. The “reentrant” ferromagnetic to “spin-glass” transition found in zero magnetic field persists in small fields. The equilibrium magnetization displays a maximum as a function of temperature in the reentrance region. The characteristic S-shape of the magnetization versus field in the “spin-glass” region and magnetic hysteresis are observed. In addition, some exact results concerning the problem of the lower critical dimension of the short-range model are derived.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:140:y:1987:i:3:p:450-477

DOI: 10.1016/0378-4371(87)90076-8

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