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Journal of the Physical Society of Japan

Static Properties of the Transverse Ising Model with Substitutional Disorder

Kazushige Mori

Published Nov 1, 1981• 2 citations

Abstract

On the basis of the effective Hamiltonian method the static properties of the transverse Ising model with substitutional disorder have been investigated. By a perturbation expansion of the density matrix the self-consistent equation for the effective field is obtained in an analytical form. The transition temperature and the susceptibility etc. are derived from the partition function and numerically calculated. It is shown that for the diluted systems this approximation gives much lower transition temperatures and higher critical concentrations than the simple ones previously derived. In the two-component system with a strong transverse field a finite critical concentration is predicted in contrast to the previous studies. The application of this approximation to the “pseudo” one-dimensional systems having weak interchain correlations is also discussed.

DOI: 10.1143/jpsj.50.3688

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On the basis of the effective Hamiltonian method the static properties of the transverse Ising model with substitutional disorder have been investigated. By a perturbation expansion of the density matrix the self-consistent equation for the effective field is obtained in an analytical form. The transition temperature and the susceptibility etc. are derived from the partition function and numerically calculated. It is shown that for the diluted systems this approximation gives much lower transition temperatures and higher critical concentrations than the simple ones previously derived. In the two-component system with a strong transverse field a finite critical concentration is predicted in contrast to the previous studies. The application of this approximation to the “pseudo” one-dimensional systems having weak interchain correlations is also discussed.

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The effect of a random transverse field on the phase transitions of a ferromagnetic spin 1/2 Ising film is investigated within a finite cluster approximation with an expansion technique for the cluster identities of spin 1/2 systems. The phase diagrams are determined as a function of the transverse field for different values of the concentration p of the disorder of the latter. It is found that at very low temperatures the ferromagnetic order is destroyed under the effect of the transverse field only if the concentration is larger than a critical value pc, which is independent of the film thickness.

The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.