Abstract
A new approach in the investigation of the order parameter behaviour near ferroelectric phase transition point is suggested. The short range and dipole interactions between particles are taken into account. The logarithmic corrections and effective critical exponents are calculated and discussed.
Highlights
The present paper has been prepared on the occasion of M.P
The problem is in the choice of the basic distribution for CV and the form of layer-by-layer integration in the CV-space
We present only the recursion relations for coefficients of consequent basic distributions, which determine the critical character of fluctuation processes near Tc in a ferroelectric cluster system with dipole-dipole interactions
Summary
The present paper has been prepared on the occasion of M.P. Kozlovskii’s 60-th anniversary, a prominent physicist and specialist in the phase transition theory. The advantage of the CVM, as compared with other methods, is a possibility to obtain the universal characteristics near the phase transition point (critical exponents and critical amplitudes ratio) and non-universal ones (i.e., expressions for different thermodynamic functions) [1, 2] In those investigations, the Ising model and the n-component model with a spherical-symmetric potential of interparticle interaction were presented. Ρλ(k, ν) is a CV, corresponding to Y i (Rq ) operator in quasimomentum-frequency representation; Φλ(k) is a Fourier transform of the intercluster dipole-dipole potential; β = 1/kT , k is the Boltzmann constant, T is the absolute temperature; Mλ, Mλ1λ2 , Mλ1λ2λ3 , Mλ1λ2λ3λ4 are cluster cumulants of first, second, third and fourth order, ωλ(k, ν) are variables conjugated to ρλ(k, ν); Z0 is a partition function of non-interacting part of the Hamiltonian (2.1). The equation of state will be obtained
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