Investigation of the Ising-type models within cluster approach

Abstract

The method for calculation of the correlation functions of the Isingtype systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin S z = ±1) the expressions for pair and ternary correlation functions within two-particle approximation in q-space are obtained for the hypercubic Bravais lattices. In the 1D case the exact expressions for them in the site space is obtained as well. On the basis of the Glauber equation within two-particle cluster approximation the longitudinal dynamical susceptibility χ(q, E) is found. In the 1D case and in the absence of external field the expression for χ(q, E) is exact. For the Emery-Blume-Griffiths model (S z = −2, 0, 2) within two-particle approximation the pair correlation functions are calculated. The fourparticle cluster approximation is used for calculation of static susceptibility χ(q) of KD 2 P O 4 ferroelectrics.

Thermodynamics and dynamical properties of the KH_{2}PO_{4} type ferroelectric compounds. A unified model

“…As we have already mentioned, the same conclusion was made in [54] within the framework of a simpler model. Later [115,116] the deuteron distribution functions and components of the static dielectric permittivity tensor of the KD 2 PO 4 type ferroelectrics and ND 4 D 2 PO 4 type antiferroelectrics were calculated within the FPCA.…”

“…For quantum reference pseudospin systems, a consistent formulation of the cluster expansion method was proposed for the first time. A method was suggested that permits within the cluster approximation to obtain the Ornstein-Zernike type equations for reference temperature cumulant Green's functions of an arbitrary order [26,116,141,142].…”

Proton Ordering Model of Phase Transitions in Hydrogen Bonded Ferrielectric Type Systems: The Gpi Crystal

“…Such an interaction can be quite large in GPI, since redistribution of protons on the bonds is accompanied by deformation and reorientation of ionic groups connected by the bonds [3]. The procedure applied below is well known and accepted for the quasione-dimensional systems (see [17,18]) and corresponds to the two-particle cluster approximation [19,20].…”

Reference Approach in Theory of Pseudospin Systems

“…The obtained there results are valid in paraphase only. Later, a method was proposed [47,48], which allows one to obtain Ornstein-Zernike type equations for an arbitrary order correlation functions of Ising models. These equations for pair and three-particle correlation functions were derived and solved within the two-particle cluster approximation (TPCA).…”

“…It was shown that the proposed in Refs. [47,48] cluster approach to calculation of correlation functions of the reference Ising models yields known exact results [31,32] for pair and three-particle correlation functions of the one-dimensional Ising model.…”