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physica status solidi (b)

Phase diagrams of the spin‐1/2 transverse ising model with random interactions

E. El Mir, M. Saber

Published May 1, 1994• 5 citations
Publisher

Abstract

Abstract The phase diagrams of the spin‐1/2 transverse Ising model with random interactions are investigated within the framework of the effective field theory using an improved configurational averaging procedure. General formulae, applicable to lattices with coordination number z, are given. Numerical results are presented for a simple cubic lattice. It is found that the effects of a transverse field on the phase diagrams exhibit a number of interesting phenomena.

DOI
10.1002/pssb.2221830120

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Abstract The phase diagrams of the spin‐1/2 transverse Ising model with random interactions are investigated within the framework of the effective field theory using an improved configurational averaging procedure. General formulae, applicable to lattices with coordination number z, are given. Numerical results are presented for a simple cubic lattice. It is found that the effects of a transverse field on the phase diagrams exhibit a number of interesting phenomena.
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.
Abstract A method in Ising models is introduced by using the effective field theory (EFT) with correlations. In the present method, for the spin‐1 Ising ferromagnetic systems with three coordination numbers q (q = 3, 4 and 6), we have derived a set of linear equations by taking as a basis the thermal averages of a central spin and a perimeter spin at the site i, which is defined within spin identities and differential operator technique. By solving numerically the set of linear equations derived individually for the Ising systems, we have evaluated the phase diagrams of both the spin‐1 Ising ferromagnetic systems with a single‐ion anisotropy and the spin‐1 transverse Ising ferromagnetic systems with a transverse field. The present results of critical transverse field for the spin‐1 transverse Ising systems improve those obtained by the pair approximation. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.