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Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

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  • Morita, T.

Abstract

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.

Suggested Citation

  • Morita, T., 1981. "Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 620-630.
    • Handle: RePEc:eee:phsmap:v:105:y:1981:i:3:p:620-630
    DOI: 10.1016/0378-4371(81)90115-1
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    References listed on IDEAS

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    1. Katsura, Shigetoshi & Nagahara, Izuru, 1980. "Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 397-416.
    2. Shimada Haruo & Nishikawa Shunsaku, 1980. "Eine Analyse des japanischen Beschäftigungssystems und des Arbeitsmarktes für Jugendliche," Zeitschrift für Wirtschaftspolitik, De Gruyter, vol. 29(1), pages 71-90, January.
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