New effective-field theory for the Blume-Capel model

Abstract

A new type of effective-field theory that has recently been used with success for many applications concerning the usual two-state Ising model is herein extended to the Blume-Capel model. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximate version, in which spin-spin correlations are neglected. It is shown that this approximative procedure, although analytically simple, provides in particular a vanishing critical temperature for one-dimensional systems and leads to results quite superior to those currently obtained within the Molecular Field Approximation for higher-dimensional systems. Within this framework we discuss as functions of temperature and for any values of the anisotropy parameter D, the order parameter, the thermal average of the square of the single-site spin variable, the internal energy and the specific heat as well as the ferromagnetic-phase stability limit. Whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement is observed with results available in the literature in which more sophisticated treatments are used. In particular, our result for the tricritical point at which the system exhibits a first-order phase transition is in quite good agreement with those obtained by using Series Expansion Methods.