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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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Quasi-Gaussian approximation: Universality, critical dimension

Quasi-Gaussian approximation: Universality, critical dimension

Chapter:
(p.179) 8 Quasi-Gaussian approximation: Universality, critical dimension
Source:
Phase Transitions and Renormalization Group
Author(s):

Jean Zinn-Justin

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199227198.003.0008

This chapter examines the universal properties of phase transitions in the quasi-Gaussian or mean-field approximations. It studies the singularities of thermodynamic functions at the transition point as well as the large-distance behaviour of the two-point correlation function. It summarizes the universal properties in the form of Landau′s theory. It stresses the peculiarities of models with continuous symmetries at low temperature due to the appearance of Goldstone modes. Finally, it evaluates corrections to the quasi-Gaussian approximation and shows that the approximation is only consistent in space dimension larger than four. Exercises are provided at the end of the chapter.

Keywords:   phase transitions, Gaussian approximation, mean-field approximation, universality, space dimensions

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