Critical properties study of exactly solved spin models for ferromagnets and ferroelectics

Abstract

Development of the hydrokinetic models of superdense matter and systems with phase transition points of a critical type is of great fundamental interest. The exact analytical expressions for the critical exponents of the model with the surface tension are known for the case of critical and tricritical points, that enables to fix their parameters directly, depending on the universality class, as well as demonstrate the possibility of non-Fisher’s universality classes where the conventional scaling relations are violated. The thermodynamic method for the investigation of critical states allows determining the type of critical behavior and the behavior of all thermodynamic quantities characterizing the system under consideration, depending on the values of a critical slope of the phase equilibrium curve and adiabatic coefficients of stability even when information of the system is limited. In this work, the critical properties of certain spin models were examined. The properties of the two-dimensional exactly solvable Lieb and Baxter models in the critical region are considered. From the point of view of the thermodynamic stability, the behavior of adiabatic and isodynamic parameters for these models is analyzed, and the types of their critical behavior are determined. The reasons for the violation of the scaling law hypothesis and the universality hypothesis for the models are clarified. It is shown that the type of phase transition depends on the value of the interaction parameter.