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Journal of Physics Condensed Matter

Longitudinal and transverse random-field Ising model

Yong‐Qiang Wang, Zhen‐Ya Li

Published Nov 14, 1994• 11 citations
Publisher

Abstract

The Ising model with both random longitudinal and transverse fields is studied by combining the pair approximation with the discretized path integral representation. The phase diagrams of the spin S= 1/2 system are obtained; the relations between the critical temperature and the local structure as well as the tricritical and re-entrant phenomena are discussed.

DOI
10.1088/0953-8984/6/46/023

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The Ising model with both random longitudinal and transverse fields is studied by combining the pair approximation with the discretized path integral representation. The phase diagrams of the spin S= 1/2 system are obtained; the relations between the critical temperature and the local structure as well as the tricritical and re-entrant phenomena are discussed.
In this paper, we propose a new method, which combines the pair approximation with the discretized path-integral representation, to study the quantum transverse Ising model with random-field. Full phase diagrams are obtained for various random-field distributions. When applied random fields are trimodal (and bimodal), the critical properties including the possibility of the existence of the tricritical points and rcentrance phenomena are numerically analyzed in detail. In the limit z→∞, the extended mean-field result is recovered.
The transverse-random-field mixed Ising model consisting of arbitrary spin values has been studied by combining the pair model approximation with discretized path-integral representation. The phase diagrams of systems with mixed spins: \ensuremath{\sigma}=1/2, S=1; \ensuremath{\sigma}=1/2, S=3/2, and \ensuremath{\sigma}=1, S=2 are plotted. Not only the discontinuity at T=0 K is found between the trimodal and bimodal distributions of transverse fields, which is similar to the single-spin counterpart, but also the tricritical behavior is observed in these phase diagrams when both transverse fields are trimodal distributed, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values. \textcopyright{} 1996 The American Physical Society.
The quantum spin system with a random field has been investigated by combining the pair approximation with the discretized path-integral representation. Second-order transition lines and tricritical points are obtained for the bimodal random-field distributions. Reentrant phase transitions, which may be caused by the competition between quantum effects and the randomness, occur with appropriate ranges of the transverse field and the random field. These results obtained with this approximation are qualitatively different from those of the ordinary mean-field approximation and display that the pair approximation takes into account the local structure of the interaction pattern of the underlying system, which results in coordinate-dependent phase diagrams.