Cluster algorithms of the Monte Carlo method, finite-size scaling, and critical exponents of complex lattice models

Abstract

For the first time, cluster algorithms of the Monte Carlo method are used to investigate critical properties of microscopic models of real ferromagnetic gadolinium. On the basis of the finite-size scaling theory, the critical exponents of the heat capacity α, magnetization β, susceptibility γ, and Fisher index η are calculated. Specific features, character, and the degree of influence of two types of weak relativistic interactions on the critical properties of gadolinium models are determined when both these interactions are taken into account. It is shown that cluster algorithms of the Monte Carlo method provide an effective tool for studying critical properties of complex models involving crossovers.