Method of calculating the critical temperature of three-dimensional Ising-like system using the non-gaussian distribution

A method for calculating the phase transition temperature Tc based on the theoretical description of the critical behaviour of the model system on the microscopic level is proposed. The main idea of such a calculation is on based a systematic consideration of the influence of the short‐ and longwavelength fluctuations of the spin density on the value of the phase transition temperature. The equation for Tc is obtained as a result of the analysis of recursion relations for the coefficients of Landau‐Ginzburg‐Wilson‐type “effective forms” and consideration of their singular properties in the critical region. As the interaction potential we use an exponentially decreasing function with effective range b. The equation for the critical temperature is obtained and the value of Tc is calculated. The dependence of Tc on the ratio b/c (c is the lattice constant) is investigated. We obtain the value βcJ = 0.211 in the case when the Ising model is approximated by the quartic measure density (ϱ4 model) and for nearest‐neighbours interaction with the interaction constant J. [Russian Text Ignore]