Phase Transitions in Low-Dimensional Disordered Potts Models

Abstract—The Monte Carlo method is used to study phase transitions in disordered two-dimensional Potts models in which disorder is realized as nonmagnetic impurities. The temperature dependences of the thermodynamic parameters have been calculated for specific heat C, susceptibility χ, and fourth-order Binder cumulants in the dependence on spin concentration p. The calculations have been performed for the system with periodic boundary conditions. The systems with linear sizes L × L = N, L = 20–160 are considered. The incorporation of nonmagnetic impurities to a spin system is shown to possibly lead to a change of the first-order phase transition to a second-order phase transition. The problem of the universality classes of the critical behavior of low-dimensional diluted systems is discussed.