Two-Particle Cluster Approximation for Ising Type Model With Arbitrary Value of Spin. Correlation Functions of Blume-Emery-Griffiths Model

In memory of Professor Roman Levitskii: 1943-2022

“…Roman Levitskii Prof. Roman Levitskii's scientific achievements ranged from developing abstract mathematical approaches and investigating complex model spin systems with different types of interactions [3][4][5][6][7] to applying the developed techniques and describing experimental data for real objects, in particular, the ferroic crystals. For instance, the reference to the description of systems, where both shortrange and long-range interactions are present, was proposed [8,9], which allows to appropriately take these interactions into account.…”

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

“…The correlation functions can be found by differentiating the free enerqy (4) of the system in nonuniform external fields (Γ i , D i ) with respect to these fields. In the case of a ∆-dimensional hypercubic lattice the matrix of pair correlation functions (in the uniform fields case) in k-space has the form [10,11]:…”

“…For compounds described by pseudospin models with essential short-range correlations, the cluster approximation (CA) [10,11,[22][23][24] is the most natural many-particle generalization of the MFA. CA not only essentially improves the MFA results for the Ising type model, but also is correct at those values of the parameters, at which MFA gives qualitatively incorrect results.…”

“…This model has been extensively studied not only because of the relative simplicity with which approximate calculations for the model can be carried out and tested as well as of the fundamental theoretical interest arising from the richness of the phase diagram that is exhibited due to competition of interactions, but also because versions and extensions of the model can be applied for the description of simple and multi-component fluids [2][3][4], dipolar and quadrupolar orderings in magnets [4][5][6], crystals with ferromagnetic impurities [4], ordering in semiconducting alloys [7], etc. The model has been studied within mean-field approximation (MFA) [1][2][3][4][5], two-particle cluster approximation (TPCA) [8][9][10][11], effective field theory [12][13][14][15], high-temperature series expansions [16], position-space renormalization group calculations [17], and Monte…”