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physica status solidi (b)

Thermodynamical Properties of the Diluted Transverse Ising Model with Anisotropic Coupling Constants

J. A. Plascak

Published Nov 1, 1983• 25 citations
Publisher

Abstract

Abstract The thermodynamical properties of the site‐ and bond‐diluted transverse Ising model with anisotropic coupling constants are studied by using a variational procedure based on Bogolyubov's inequality. Within this approach the thermal behaviour of the system is obtained in the entire range of temperature (0 ≤ T < ∞). The results for the critical temperature, critical transverse field, and critical concentration are, in several cases, comparable to the constant‐coupling approximation.

DOI
10.1002/pssb.2221200124

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Journal of Physics C Solid State Physics•Jun 10, 1986•25 citations
Abstract The thermodynamical properties of the site‐ and bond‐diluted transverse Ising model with anisotropic coupling constants are studied by using a variational procedure based on Bogolyubov's inequality. Within this approach the thermal behaviour of the system is obtained in the entire range of temperature (0 ≤ T < ∞). The results for the critical temperature, critical transverse field, and critical concentration are, in several cases, comparable to the constant‐coupling approximation.
The effect of random bond (site) dilution on the phase transition of a three-dimensional transverse Ising model is studied by a cluster variation, along with perturbation expansion method. Complete phase diagrams in the temperature-concentration-transverse-field space are constructed for both the cases. The value of critical transverse field as a function of concentration, at zero temperature, exhibits a discontinuity at the critical value of concentration for the existence of phase transition, as conjectured by Harris. As is expected for the existence of a second-order phase transition, the static susceptibility diverges on the critical surface.
The authors study both the pure anisotropic and the anisotropically diluted transverse Ising model at zero temperature on the square lattice. In the former the coupling along each Cartesian direction are allowed to be different, whereas in the latter it is the bond concentration which may be different along the Cartesian directions. By means of a position space renormalisation group scheme, they find that in both cases the isotropic systems are stable with respect to anisotropy perturbations. They also discuss their results in view of a recently proposed criterion for the stability of pure systems of fixed points with respect to correlated dilution.
Recently, there has been interest in the problems of disorder in the Ising model in a transverse field, which may apply to DKDP-KDP mixed systems and diluted vanadates. The site and bond diluted transverse Ising models have already been studied using Green's function techniques along with the coherent potential approximation. However, the situation as regards to the existence of a second order phase transition and the divergence of the static susceptibility is not very clear. In the present paper, a spin ½ Ising model in a transverse field and random bond (site) dilution is studied by variational cluster and perturbation expansion method. The critical temperature for the existence of a second order phase transition is calculated as a function of concentration of bonds (spins) and the transverse field. Variation of the critical concentration, for the existence of phase transition, is studied as a function of the transverse field. A phase diagram in the temperature-concentration-transverse field space is constructed. The static susceptibility is calculated and is found to diverge at the critical temperature, as is expected for the existence of a second order phase transition.