Study of the critical behaviour of three-dimensional Ising-like systems on the basis of the  ⁶model with allowance for microscopic parameters: I. High-temperature region

Abstract

The behaviour of a three-dimensional Ising-like system at temperatures above the critical value of T c is studied in the approximation of the sextic distribution for modes of spin density oscillations (ρ 6 model). The original collective variables method is developed in this higher non-Gaussian approximation for calculating the thermodynamic characteristics of the system near T c taking into account the first confluent correction. The calculations are illustrated by an example of a simple cubic lattice and an exponentially decreasing interaction potential. The main distinctive feature of the method is the separate inclusion of the contributions to the thermodynamic functions from the short-wave and longwave spin density oscillation modes. The dependences of the phase transition temperature, leading critical amplitudes, and correction-to-scaling amplitudes for the specific heat and susceptibility on the microscopic parameters of the system are investigated.

Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

“…The advantage of the CV method lies in the possibility of obtaining and analysing thermodynamic characteristics as functions of the microscopic parameters of the initial system [10,11,15,19,20]. The results of calculations for a 3D Ising system on the basis of the ρ 4 and ρ 6 models are in accord with the results obtained by other authors.…”

“…The present paper supplements the earlier works [8][9][10][11], in which the ρ 6 model was used for calculating the free energy and other thermodynamic functions of the system in the absence of an external field. The ρ 6 model provides a better quantitative description of the critical behaviour of a 3D Ising-like magnet than the ρ 4 model [10].…”

“…For the Fourier transform of the interaction potential, we use the following approximation [2,10,11]:…”

“…The values of s close to s * are optimal for the given method of calculations. The difference form of the recurrence relations (RRs) between the coefficients of effective non-Gaussian densities of measures operates successfully just in this region of s. It was established (see, e.g., [10,11]) that as the form of the density of measure becomes more complicated, the dependence of the critical exponent of the correlation length ν on the RG parameter s becomes weaker gradually, and, starting from the sextic density of measure, the value of the exponent ν, having a tendency to saturate with increasing m (which characterizes the order of the ρ 2m model, m = 2, 3, 4, 5), changes insignificantly (see Figures 1 and 2). The point s ≈ s * in Figure 1 corresponds to the beginning of the ν(s) curve stabilization for each of the ρ 2m models.…”

Free energy and equation of state of Ising-like magnet near the critical point

“…Secondly, the average value of the variable ρ 0 is the order parameter of the system [9,10]. Thus, performing the substitution of the variable ρ 0 = √ Nρ 0 and evaluating the integral (19) by the steepest-descent method, we obtain the expression for the system free energy…”