Phase Transitions
摘要
Interacting systems display a variety of phases as a consequence of collective phenomena. Often, spontaneous symmetry breaking is associated with phase transitions. In this chapter, we focus on classical phase transitions. Several examples are given and a classification of phase transitions is presented. The Landau theory of phase transitions is presented and a mean-field approach is used to characterize different phases. Several conditions on the phases and their transitions are presented such as the Gibbs phase rule, the Lee-Yang theory, the existence of Goldstone bosons in the ordered phase, the Anderson-Higgs mechanism, and the Hohenberg-Mermin-Wagner theorem. The case of second-order phase transitions is discussed in some length, and the concept or an order parameter and the critical behavior near the phase transition are discussed. The case of a first-order phase transition is also discussed, with a digression through metastable and unstable states. The growth of a stable phase inside a metastable or unstable phase, considering nucleation and the growth of droplets of the stable phase, is discussed.