Fluctuations in the paraphase of improper ferroelastics taking into account indirect interactions through the field of elastic deformations

Abstract

The effect of indirect interactions (through the field of elastic deformations) on the temperature dependences of a two-point correlator of the order parameter of an improper ferroelastic is studied theoretically taking into account the interaction of fluctuations at different spatial points with one another and with defective elastic fields. The latter are accounted for by using a phenomenological field of the sources of defective elastic fields. Analysis is carried out using diagrammatic expansions followed by a transition to the Dyson equation. It is proposed that the Dyson equation be approximately solved nonperturbatively using the ansatz for an exact two-point Green function of the form Gint(k)=T/[αij(τ)kikj+β(τ)]. Such an approach makes it possible to reduce the problem to solving a system of nonlinear algebraic equations, which can effectively be solved by numerical methods. The aggregate of the assumptions made is equivalent to the mean field theory, which, however, cannot be reduced in the present case to the Ginzburg-Landau theory in view of the essentially nonlocal character of the indirect interaction via the field of elastic deformations. The results of numerical calculations are considered for a defect-free Hg2Cl2 crystal, for which it is shown that parameters of dispersion αij acquire a substantial temperature dependence in a temperature range much broader than the width of the critical region of the given crystal.