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Phase Transitions and Renormalization Group$
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Jean Zinn-Justin

Print publication date: 2007

Print ISBN-13: 9780199227198

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199227198.001.0001

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Phase transitions: Generalities and examples

Phase transitions: Generalities and examples

(p.147) 7 Phase transitions: Generalities and examples
Phase Transitions and Renormalization Group

Jean Zinn-Justin

Oxford University Press

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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