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physica status solidi (b)

One‐ and Two‐Spin Cluster Approximations for the Site‐Diluted Spin‐1 Ising Model

A. Bobák, S. Mockovčiak, J. Sivuľka

Published Apr 1, 1993• 12 citations
Publisher

Abstract

Abstract One‐ and two‐spin cluster approximations employing the differential operator technique are applied to study the second‐order phase boundaries for a quenched site‐diluted spin‐1 Ising model. The critical concentration below which the transition temperature reduces to zero is determined for the honeycomb, square, and simple cubic lattices. The results are compared to those of the site‐diluted spin‐1/2 Ising model.

DOI
10.1002/pssb.2221760221

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Abstract One‐ and two‐spin cluster approximations employing the differential operator technique are applied to study the second‐order phase boundaries for a quenched site‐diluted spin‐1 Ising model. The critical concentration below which the transition temperature reduces to zero is determined for the honeycomb, square, and simple cubic lattices. The results are compared to those of the site‐diluted spin‐1/2 Ising model.
Abstract The quenched site‐dilute Ising model in two and three dimensions is studied by employing the effective‐field renormalization‐group method. The concentration dependence of the critical temperature and values of the critical concentration are obtained and compared to other different methods. Quite good results for a honeycomb lattice are achieved even by considering the smallest possible clusters. In particular, it is shown that the present formalism is able to distinguish between lattices of the same coordination number but of different dimensions.
Site diluted spin-1/2 Ising and spin-1 Blume Capel (BC) models in the presence of transverse field interactions are examined by introducing an effective-field approximation that takes into account the multi-site correlations in the cluster of a considered lattice with an improved configurational averaging technique. The critical concentration below which the transition temperature reduces to zero is determined for both models, and the estimated values are compared with those obtained by the other methods in the literature. It is found that diluting the lattice sites by non magnetic atoms may cause some drastic changes on some of the characteristic features of the model. Particular attention has been paid on the global phase diagrams of a spin-1 BC model, and it has also been shown that the conditions for the occurrence of a second order reentrance in the system is rather complicated, since the existence or extinction of reentrance is rather sensitive to the competing effects between D/J, Ω/J and c.
A finite cluster effective-field theory in which the single-site kinematic relations are treated exactly is applied to a study of the spin-one Ising ferromagnet on a honeycomb lattice. The Ising model studied contains both biquadratic exchange, J′ and single-ion anisotropy D in addition to the usual bilinear exchange interactions J. The second-order phase boundary is studied for a range of interaction strengths and the results compared to those of other methods. The dependence of the results on cluster size is investigated. The magnetization predicted by the four-site cluster theory for a selection of single-ion anisotropy strengths is also compared with exact results that have recently been deduced in the subspace J′/J=−[ln cosh(βJ)]/(βJ). In extending the theory to account for site dilution, a form of configurational averaging is adopted that is superior to that of earlier authors. The variation with site dilution of the tricritical point in the T-D plane is reported.
The thermal and magnetic properties of the simple cubic Ising model with random, quenched, site impurities have been determined by Monte Carlo calculations. The transition appears to remain sharp, and the critical temperature decreases monotonically towards zero as the impurity concentration is increased towards the percolation limit. No clear evidence is found for any change in the critical exponents away from the pure lattice values. These results are discussed in terms of Harris's predictions for the critical behavior of impure systems.
Using the Monte Carlo technique the authors have studied a two-dimensional Ising model with quenched non-magnetic impurities. In particular they calculated the temperature dependence of the order parameter, of the zero-field susceptibility and of the specific heat. These results indicate that a second-order phase transition is preserved for p>or=0.9 where 1-p denotes the concentration of randomly distributed non-magnetic sites. Moreover, they yield beta approximately=1/8 and gamma approximately=7/4, indicating that these exponents equal the corresponding ones for the pure Ising model.