Equilibrium Phase Transitions in Statistical Physics

Abstract

A principal objective in the study of equilibrium phase transitions is to capture the transitions from one equilibrium to another and to study the nature or order of such transitions. The study of equilibrium phase transitions presented in this book involves a combination of modeling, mathematical analysis, and physical predictions. First, the standard model for a thermodynamic system is derived using the recently discovered potential-descending principle (PDP), addressed in Chap. 7. Second, all equilibrium phase transitions are fully characterized by three basic theorems. Third, the dynamical law of fluctuations is derived, and we show that the standard model, together with the dynamic law of fluctuation, offers correct information for critical exponents. Fourth, the theory is applied to gas-liquid transitions, ferromagnetism, binary systems, superconductivity, and liquid heliums, leading to various physical predictions and insights to the underlying physical problems.