No 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.

The analytic method for deriving the equation of state of a cell fluid model in the region above the critical temperature (T T c ) is elaborated using the renormalization group transformation in the collective variables set.Mathematical description with allowance for non-Gaussian fluctuations of the order parameter is performed in the vicinity of the critical point on the basis of the ρ 4 model. The proposed method of calculation of the grand partition function allows one to obtain the equation for the critical temperature of the fluid model in addition to universal quantities such as critical exponents of the correlation length. The isothermal compressibility is plotted as a function of density. The line of extrema of the compressibility in the supercritical region is also represented.

The behavior of a 3D Ising system at temperatures above Tc is studied in the approximation of sextic distribution for modes of spin moment density oscillations (ρ6 model). An original method is developed in this higher non-Gaussian approximation for calculating the thermodynamic characteristics of the 3D Ising model near Tc taking into account the first confluent correction. The contributions to the thermodynamic functions of an Ising ferromagnet (free energy, entropy, internal energy, and specific heat) from the short-wave and long-wave modes of spin density oscillations are considered separately. A nonuniversal factor determined by microscopic characteristics of the system is singled out in the expressions for leading critical amplitudes and the amplitudes of the confluent correction. Numerical estimates of the critical region size, phase transition temperature, leading critical amplitudes, and the amplitudes of the correction to scaling of specific heat and susceptibility of the system are given for different values of effective radius of the exponentially decreasing interaction potential.