Magnetization in a quenched random-bond Ising ferromagnet with anisotropic coupling constants

Abstract

Within the framework of an effective-field theory we discuss the phase diagram (ferromagnetic-phase stability limit) and magnetization of a quenched bond-mixed spin-\textonehalf{} Ising model in an anisotropic simple cubic lattice for both competing and noncompeting interactions. Although analytically simple, the present formalism is superior to the standard mean-field approximation regarding at least two important features, namely, it is capable of providing (i) vanishing critical temperatures for one-dimensional systems, and (ii) expected nonuniform convergences in the highly diluted and highly anisotropic limits. The generality of the model under consideration permits the exhibition of a certain amount of physically interesting crossovers (dimensionality changes, dilute-nondilute behavior, or even mixed situations) at both the phase diagram and magnetization levels. Whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement is observed with results available in the literature.