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Journal of Physics Condensed Matter

The diluted mixed spin-1/2 and spin-1 Ising model in a transverse random field

Noureddine Benayad, A. Dakhama, Ahmed Fathi, R. Zerhouni

Published Apr 13, 1998• 8 citations
Publisher

Abstract

The diluted mixed-spin Ising system consisting of spin 1/2 and spin 1 with a transverse random field is studied by the use of an effective-field method within the framework of a single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. The phase diagrams are investigated for various lattice structures both for pure and diluted systems, where the transverse field is bimodally and trimodally distributed.

DOI
10.1088/0953-8984/10/14/005

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The diluted mixed-spin Ising system consisting of spin 1/2 and spin 1 with a transverse random field is studied by the use of an effective-field method within the framework of a single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. The phase diagrams are investigated for various lattice structures both for pure and diluted systems, where the transverse field is bimodally and trimodally distributed.
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The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.
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.