Field theoretical approach to the paramagnetic-ferrimagnetic transition in strongly coupled paramagnetic systems

Abstract The aim of this paper is the investigation of the critical properties of two strongly coupled paramagnetic sublattices exhibiting a paramagnetic–ferrimagnetic 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-group (RG) techniques applied to an elaborated field model describing such a transition, which is of Landau–Ginzburg–Wilson type. The associated free energy or action is a functional of two kinds of order parameters (local magnetizations), which are scalar fields ϕ and ψ relative to these sublattices. It involves quadratic and quartic terms in both fields, and a lowest-order coupling C o ϕψ , where C o >0 stands for the coupling constant measuring 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 ϕ 4 -theory ( C o =0). The existence of the renormalization theory enables us to write the RG-equations satisfied by the correlation functions. We solve these using the standard characteristics method, to get all critical properties of the system under investigation. We first determine 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 problem, namely, the wave vector q , the (renormalized) coupling C and the temperature 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 magnetic systems.