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Physical review. B, Condensed matter

Transverse Ising model with arbitrary spin

T. Kaneyoshi, M. Jaščur, I. P. Fittipaldi

Published Jul 1, 1993• 114 citations
Publisher

Abstract

An effective-field theory that has recently been used for studying higher-spin Ising models is herein extended to the transverse Ising model with an arbitrary spin S. The general formulation for evaluating the transition line in the \ensuremath{\Omega}-T space and relevant statistical-mechanical quantities is derived. Numerical results are performed and analyzed for the particular cases S=3/2 and S=2.

DOI
10.1103/physrevb.48.250

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An effective-field theory that has recently been used for studying higher-spin Ising models is herein extended to the transverse Ising model with an arbitrary spin S. The general formulation for evaluating the transition line in the \ensuremath{\Omega}-T space and relevant statistical-mechanical quantities is derived. Numerical results are performed and analyzed for the particular cases S=3/2 and S=2.
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A theoretical study of a mixed spin- and spin- Ising system with independent transverse fields is present- ed using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the lon- gitudinal and transverse components of the magnetization and its higher moments is also studied.
The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the multi-spin correlations systematically in a representative manner, as well as its single site counterparts in the system and gives results for the critical temperature of the system much better than those of the other works in the literature. The formulation can be easily applied to various extensions of s-1/2 Ising models, as long as the system contains only the nearest neighbor interactions as spin-spin interactions.