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Physical review. B, Condensed matter

Reentrant phase transitions in a quantum spin system with random fields

Terufumi Yokota, Yūki Sugiyama

Published Apr 1, 1988• 28 citations
Publisher

Abstract

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 ${h}_{0}$.

DOI
10.1103/physrevb.37.5657

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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​.
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.
The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations. We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z , when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.
The bimodal random field quantum spin-32\frac{3}{2}23​ Ising system is investigated by combining the pair approximation with the discretized path-integral representation. The second-order phase transition lines, and tricritical points are obtained for the bimodal random field distribution. Reentrant phase transitions, which may be caused by the competition between quantum effects and randomness, are observed. The phase diagrams with respect to the random field and the second-order phase transition temperature, i.e., (H, T) plane, are studied extensively for given values of the transverse field G and the coordination number z.
Phase diagrams and magnetization curves of a diluted spin-1 transverse Ising model in a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The behavior of the tricritical point is also examined as a function of applied transverse field. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.