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physica status solidi (b)

On the random transverse field mixed spin Ising model of spin‐1/2 and spin‐1

X. M. Weng, Z. Y. Li

Published Oct 1, 1996• 9 citations
Publisher

Abstract

Abstract The critical behavior of mixed spin Ising model is investigated when the transverse fields are randomly distributed. The calculation shows that when the transverse fields are both bimodally distributed, the transition temperature decreases with increasing transverse field and eventually vanishes at a finite field. When one of the transverse fields is bimodally and the other trimodally distributed, the temperature decreases but does not vanish. When both transverse fields are trimodally distributed, the transverse field dependence of temperature breaks off and a tricritical point appears due to the interaction between quantum fluctuations and disorder.

DOI
10.1002/pssb.2221970223

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Communications in Theoretical Physics•Oct 15, 2004•10 citations
Abstract The critical behavior of mixed spin Ising model is investigated when the transverse fields are randomly distributed. The calculation shows that when the transverse fields are both bimodally distributed, the transition temperature decreases with increasing transverse field and eventually vanishes at a finite field. When one of the transverse fields is bimodally and the other trimodally distributed, the temperature decreases but does not vanish. When both transverse fields are trimodally distributed, the transverse field dependence of temperature breaks off and a tricritical point appears due to the interaction between quantum fluctuations and disorder.
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.
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.
We determine the phase diagram of the transverse Ising model with a trimodal distribution (sum of three \ensuremath{\delta} functions) for a longitudinal random field at T=0, using a mean-field approximation. The phase diagram includes tricritical points, ordered critical points, a fourth-order point, critical end points, and a double critical end point. Our T=0 phase diagram is completely equivalent to the one obtained by Kaufman, Klunzinger, and Khurana for the random-field Ising model. We show that the temperature and the magnitude of the transverse field play a similar role.
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.