Comparative Study on the Phase Transition Behaviors of Fractional Molecular Field Theory and Random-Site Ising Model

Fractional molecular field theory (FMFT) is a phenomenological theory that describes phase transitions in crystals with randomly distributed components, such as the relaxor-ferroelectrics and spin glasses. In order to verify the feasibility of this theory, this paper fits it to the Monte Carlo simulations of specific heat and susceptibility vs temperature of two-dimensional random-site Ising model (2D-RSIM). The results indicate that FMFT deviates from 2D-RSIM significantly. The main reason for the deviation is that 2D-RSIM is a typical system of component random distribution, where the real order parameter is spatially heterogeneous and has no symmetry of space translation, but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.