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physica status solidi (b)

Effective‐field renormalization‐group approach for quenched site‐dilute ising models

A. Bobák, M. Jaščur, S. Mockovčiak

Published Jun 1, 1994• 4 citations
Publisher

Abstract

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.

DOI
10.1002/pssb.2221830223

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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.
A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.
A simple modification of the real-space renormalisation group method is used to discuss critical behaviour of site diluted spin- 1 / 2 Ising and Heisenberg ferromagnets in two and three dimensions. The critical parameters and critical exponents are evaluated, and are shown to be in good agreement with the exact results and series calculations for site-diluted Ising ferromagnets on the square and triangular lattices. Good values of the critical parameters have also been obtained for the site-diluted Heisenberg and Ising models in two and three dimensions using the Migdal-Kadanoff approximation (1976).