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

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

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.

Suggested Citation

  • De Smedt, Ph. & Indekeu, J.O. & Zhang, L., 1987. "The short-range van Hemmen model in a simple Kikuchi approximation: Comparison with the mean-field model and with spin-glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(3), pages 450-477.
    • Handle: RePEc:eee:phsmap:v:140:y:1987:i:3:p:450-477
    DOI: 10.1016/0378-4371(87)90076-8
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    References listed on IDEAS

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    1. Katsura, Shigetoshi & Matsuno, Akira, 1983. "The transition from the spin-glass to the ferromagnetic state in the bond-random Ising model in the face-centred cubic lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 483-488.
    2. D. Weiserbs & N. Kuzondisa, 1983. "Application d'une version dynamique de la fonction de coût quadratique généralisée à la demande de facteurs énergétique," Discussion Papers (REL - Recherches Economiques de Louvain) 1983014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Soliman, Ibrahim & El Nagar, Refaat, 1981. "السياسات التمويلية فى مجال الانتاج الحيوانى بالاشارة الى محافظة الشرقية," Conference Papers 212969, Zagazig University, Department of Agricultural Economics.
    4. Bogdanowicz-Bindert, Christine A., 1983. "Portugal, Turkey and Peru: Three successful stabilization programmes under the auspices of the IMF," World Development, Elsevier, vol. 11(1), pages 65-70, January.
    5. Canisius, J. & Van Hemmen, J.L. & Nieuwenhuizen, Th.M., 1985. "A generalized thouless formula as a criterion for Anderson localization in two- and three-dimensional systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 131(1), pages 131-156.
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