Field theoretical approach to the paramagnetic-ferrimagnetic transition instrongly coupled paramagnetic systems

The aim of this paper is the investigation of the critical properties of tw o strongly coupled paramagnetic sublattices exhibiting a paramagnetic-ferri magnetic transition, at some critical temperature T-c greater than the room temperature. In order to take into account the strong fluctuations of the magnetization near the critical point, use is made of the renormalization-g roup (RG) techniques applied to an elaborated field model describing such a transition,which is of Landau-Ginzburg-Wilson type. The associated free en ergy or action is a functional of two kinds of order parameters (local magn etizations), which are scalar fields phi and psi relative to these sublatti ces. It involves quadratic and quartic terms in both fields, and a lowest-o rder coupling C(o)phi psi where C-o > 0 stands for the coupling constant me asuring the interaction between the two sublattices. We first show that the associated field theory is renormalizable at any order of the perturbation series in the coupling constants, up to a critical dimension d(c) = 4, and that, the corresponding counterterms have the same form as those relative to the usual phi(4)-theory (C-o = 0). The existence of the renormalization theory enables us to write the RG-equations satisfied by the correlation fu nctions. We solve these using the standard characteristics method, to get a ll critical properties of the system under investigation. We first determin e the exact shape of the critical line in the (T, C)-plane, along which the system undergoes a phase transition. Second, we determine the scaling laws of the correlation functions, with respect to relevant parameters of the p roblem, namely, the wave vector q, the (renormalized) coupling C and the te mperature shift T - T-c. We find that these scaling laws are characterized by critical exponents, which are the same as those relative to Ising-like m agnetic systems. (C) 2000 Elsevier Science B.V. All rights reserved.