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Physical review. B, Condensed matter

Pair-approximation method for the quantum transverse Ising model with a random field

Yu‐qiang Ma, Zhen‐Ya Li

Published Jun 1, 1990• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.41.11392

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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.
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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.
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The transverse Ising model with random fields has been studied within the mean-field approximation extended to include quantum effects. When applied random fields are bimodal (sum of two \ensuremath{\delta} functions) and transverse fields \ensuremath{\Gamma} are not too large, tricritical points exist. In these cases, reentrant phenomena can be seen for appropriate ranges of \ensuremath{\Gamma} and random fields h0{h}_{0}h0​.