Chapter 1 introduces various essential ideas on second-order phase transitions and the theoretical challenges that accompany them. Furthermore, it focuses on important issues, for example, correlation length, correlation functions, scaling laws and behaviour, energy minimization, entropy maximization, dimensionality of space and order parameters and critical exponents, etc. It introduces and also devotes a short discussion to the Ising model and its most significant developments during the years of its study, as well as a short background about Ising himself. The chapter also contains two appendices that summarize all relevant results of ensembles of classical statistical mechanics and quantum statistical mechanics.
Ab Initio Statistical Mechanics of Structural Phase Transitions