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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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The s 4 field theory near dimension 4

The s 4 field theory near dimension 4

(p.307) 13 The s 4 field theory near dimension 4
Phase Transitions and Renormalization Group

Jean Zinn-Justin

Oxford University Press

This chapter explains how the asymptotic renormalization group equations (RGE), introduced without too much justification in Section 10.6, can be proved within the framework of statistical (or quantum) field theory. The proof is based on the methods of perturbative statistical field theory introduced in Chapter 12, and a few assumptions that it is thus possible to clarify. The discussion is restricted to theories with an Ising type symmetry and the field s has only one component. Generalization to models with N-component fields and O (N) symmetry is simple.

Keywords:   renormalization group, RGE, O(N) symmetry, quantum field theory, Ising type symmetry

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