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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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Critical Phenomena: General Considerations

Critical Phenomena: General Considerations

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter reviews a few properties, from the point of view of phase transitions, of simple ferromagnetic lattice models. In systems with finite range interactions a transfer matrix can be defined. It first examines its properties in a finite volume. In the infinite volume limit, low and high temperature considerations provide convincing evidence of the existence of phase transitions in Ising-like systems. The notion of order parameter is related to cluster properties in the low temperature broken phase. It is shown in a simple example that phase transitions indeed correspond to breaking of ergodicity. The chapter extends the analysis to ferromagnetic systems with continuous symmetries. The appendix contains a brief discussion of quenched disorder.

Keywords:   phase transitions, transfer matrix, Ising-like systems, order parameter, cluster properties, quenched disorder

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