# Phase transitions: Generalities and examples

# Phase transitions: Generalities and examples

This chapter focuses on the concept of phase transition — a concept that is far from being trivial in the sense that a phase transition requires the interaction of an infinite number of degrees of freedom. It first solves exactly a particular model in the limit in which the number of space dimensions becomes infinite. In this limit, the model exhibits a behaviour that the analysis presented in the following chapters will identify as quasi-Gaussian or mean-field like. It then discusses in general terms the existence of phase transitions as a function of the space dimension. It emphasizes the difference between models with discrete and continuous symmetries in dimension two. Exercises are provided at the end of the chapter.

*Keywords:*
phase transition, infinite temperature, infinite dimension, universality, transfer matrix, continuous symmetries

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