Pair Correlation Functions of the Ising Type Model with Spin 1 within Two-Particle Cluster Approximation

Abstract

The Blume-Emery-Griffiths model on hypercubic lattices within the twoparticle cluster approximation is investigated. The expressions for the pair correlation functions in k-space are derived. On the basis of obtained results (at k = 0) the static susceptibility of this model on the simple cubic lattice is calculated at various values of the single-ion anisotropy and biquadratic interaction.

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

“…The free energy of the spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field (1) within the TPCA reads [15,27,28]:…”

“…It proves to be efficient for simple and multicomponent fluids [11,18,19], dipolar and quadrupolar orderings in magnets [1,4,11], binary alloys of ferromagnetic and nonmagnetic components [11,20], ordering in semiconducting alloys [21]. Moreover, due to the richness of its phase diagrams [16,[22][23][24][25][26][27][28] the Blume-Emery-Griffiths model is also of a purely theoretical interest.…”

The spin 1 Blume Capel model with RKKY interactions

“…The cluster variational method in pair approximation has also been adopted in a study of the BEG model on a magnetic bilayer [20], and in a further study of the BEG model in the vicinity of the antiferromagnetic Potts line [21]. Within the same approximation (but under the name of 'two-particle cluster approximation') other works on the spin one BEG model have also been presented [22,23]. Finally, CVMPA has found application in the studies of spin 3 2 Ising models with higher-order interactions [24], and in the mixed spin 1À spin 3 2 Blume Capel ferromagnet [25].…”

“…[13][14][15][20][21][22][23][24][25] the methodology of deriving the cluster variational equations and solution has not always been the same. In Refs.…”

Order Parameter for Ferromagnetic Phase Transition in the Two-Particle Magnetic Cluster System

“…The cluster approximation in the form based on the paper [3] was used by R.R.Levitskii with collaborators in the numerous investigations concerning KDP and isomorphous crystals with hydrogen bounds [6][7][8][9][10][11][12][13][14][15][16]. The scope of his interests is very wide, i.e., from static properties to the dynamics and relaxation behaviour of the systems.…”