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physica status solidi (b)

The Random Transverse Ising Model with Spin-1/2, Spin-1 and Mixed Spins

B. Laaboudi, M. El Atri, M. Saber, M. Saber

Published Jul 1, 1998• 7 citations
Publisher

Abstract

Using the effective field theory (EFT) which takes into consideration the fluctuations of the effective field and which is based on a probability distribution of random variables which accounts for all the single kinematic relations, we have studied the transverse random field Ising model (TRIM) with spin-½ and spin-1 and the transverse random field mixed Ising model (TRMIM) with both spin-½ and spin-1. It is shown that the simplest approximation gives satisfactory results for the phase diagrams when compared with other methods.

DOI
10.1002/(sici)1521-3951(199807)208:1<197::aid-pssb197>3.0.co;2-3

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Using the effective field theory (EFT) which takes into consideration the fluctuations of the effective field and which is based on a probability distribution of random variables which accounts for all the single kinematic relations, we have studied the transverse random field Ising model (TRIM) with spin-½ and spin-1 and the transverse random field mixed Ising model (TRMIM) with both spin-½ and spin-1. It is shown that the simplest approximation gives satisfactory results for the phase diagrams when compared with other methods.
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 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.
Abstract The transverse spin‐3/2 Ising model with random interactions is studied using an effective field method within the framework of a single‐site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalized Van der Waerden identities, that account exactly for the single‐site kinematic relations. A model is adopted in which the nearest‐neighbour exchange couplings are described by the probability distribution law: P(Jij) = p δ(Jij‐J) + (1‐p) δ(Jij‐aJ). The critical temperature at which the longitudinal magnetization vanishes is studied as a function of p and the transverse field strength. The thermal variation of the longitudinal and transverse magnetizations and higher‐order magnetization moments are also studied.
In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using a probability distribution method based on the use of exact Van der Waerden identities. We present our numerical results, such as the phase diagrams, the thermal variations of the transverse magnetization, the internal energy, the magnetic specific heat as a function of different values of p, the concentration of the random transverse field. As a result, the critical values of transverse field , temperature and concentration were obtained for the square lattice.