Critical dynamics of strong coupling paramagnetic systems exhibiting a paramagnetic–ferrimagnetic transition

M. Chahid, M. Benhamou and M. El Hafidi

Physica A: Statistical Mechanics and its Applications, 2002, vol. 305, issue 3, 521-541

Abstract: The purpose of this work is the investigation of critical dynamic properties of two strongly coupled paramagnetic sublattices exhibiting a paramagnetic–ferrimagnetic transition. To go beyond the mean-field approximation, and in order to get a correct critical dynamic behavior, use is made of the renormalization-group (RG) techniques applied to a field model describing such a transition. The model is of Landau–Ginzburg type, whose free energy is a functional of two kinds of order parameters (local magnetizations) ϕ and ψ, which are scalar fields associated with these sublattices. This free energy involves, beside quadratic and quartic terms in both fields ϕ and ψ, a lowest-order coupling, −C0ϕψ, where C0 is the coupling constant measuring the interaction between the two sublattices. Within the framework of mean-field theory, we first compute exactly the partial dynamic structure factors, when the temperature is changed from an initial value Ti to a final one Tf very close to the critical temperature Tc. The main conclusion is that, physics is entirely controlled by three kinds of lengths, which are the wavelength q−1, the static thermal correlation length ξ and an extra length Lt measuring the size of ordered domains at time t. Second, from the Langevin equations (with a Gaussian white noise), we derive an effective action allowing to compute the free propagators in terms of wave vector q and frequency ω. Third, through a supersymmetric formulation of this effective action and using the RG-techniques, we obtain all critical dynamic properties of the system. In particular, we derive a relationship between the relaxation time τ and the thermal correlation length ξ, i.e., τ∼ξz, with the exponent z=(4−η)/(2ν+1), where ν and η are the usual critical exponents of Ising-like magnetic systems. At two dimensions, we find the exact value z=54. At three dimensions, and using the best values for exponents ν and η, we find z=1.7562±0.0027.

Keywords: Sublattices; Paramagnetism; Ferrimagnetism; Transition; Critical dynamics; Renormalization group; Scaling laws; Relaxation time (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:305:y:2002:i:3:p:521-541

DOI: 10.1016/S0378-4371(01)00558-1

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