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physica status solidi (b)

Investigation of Oguchi's procedure applied to the ising model

J. R. Faleiro Ferreira, N. P. Silva

Published Mar 1, 1983• 6 citations
Publisher

Abstract

Abstract Approximate critical temperature of the anisotropic ferromagnetic Ising model is calculated using the procedure proposed by Oguchi, with better results than those obtained by the use of Bogolyubov's principle. The calculation is made with linear and double chain trial Hamiltonians.
DOI
10.1002/pssb.2221160119

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To calculate thermodynamic functions in statistical mechanics the authors propose a new variational approach which has as particular cases the approaches of Bogoliubov, Oguchi and Tsallis-da Silva (1982), but introduces some improvements, mainly in the short-range order effects above the critical temperature. It requires a choice of a trial Hamiltonian that defines an approximate ensemble through which the thermodynamic functions may be calculated. To check the efficiency of their approach they apply it to the ferromagnetic Ising model by using the simplest possible trial Hamiltonian.
Abstract By pushing forward the decoupling from the three-to the four-point correlation function short-range order is systematically introduced into the description of the statistical behaviour of the Ising-model. Application of a procedure which is a natural generalization of that invented by Bogoljubov and Tjablikov for the Heisenberg-model, leads to an overall-approximation for the magnetization and the nearest-neighbour correlation which may be compared with the Ising-model variant of Oguchi's two-spin-cluster molecular field theory. The results of both approximations are very similar both for low and high temperatures, but for the transition point the new approach yields values which lie considerably lower and therefore are more reliable than those following from Oguchi's theory. Moreover, the comparison with a slight modification of the theory which is also presented in this paper, illuminates the physical mechanism which is responsible for the formation of correlations within the order of approximation, considered.