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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Non-Magnetic Systems and The (φ2)2 Field Theory

Non-Magnetic Systems and The (φ2)2 Field Theory

Chapter:
(p.675) 28 NON-MAGNETIC SYSTEMS AND THE (φ2)2 FIELD THEORY
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0028

Many systems to which the RG predictions based on the φ4 field theory apply are non-magnetic. This chapter considers three systems or classes of systems which are of special interest because they allow precise comparisons between RG results, experiments and simulations: long polymer chains (self-avoiding random walks), liquid-vapour, and superfluid Helium. It shows that their critical properties are indeed related to the N-component φ4 field theory: N = 0 describes the statistical properties of polymer chains asymptotically when the length becomes large, N = 1 and N = 2 the universal properties of the liquid-vapour and Helium super fluid transitions, respectively.

Keywords:   RG theory, field theory, non-magnetic systems, liquid-vapour phase transition, helium superfluid transition

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