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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

Quantum Field Theory and Critical Phenomena


Oxford University Press

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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