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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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Ferromagnetic systems. Correlation functions

Ferromagnetic systems. Correlation functions

(p.127) 6 Ferromagnetic systems. Correlation functions
Phase Transitions and Renormalization Group

Jean Zinn-Justin

Oxford University Press

This chapter defines more general statistical systems in an arbitrary number of space dimensions. For convenience, it uses the ferromagnetic language — even though, as a consequence of universality, the results that are derived in this work apply to much more general statistical systems. In addition to complete and connected correlation functions (whose decay properties at large distance — called cluster properties — are recalled), it introduces vertex functions, which are related to the thermodynamic potential. The free energy and thermodynamic potential, like connected correlation functions and vertex functions, are related by a Legendre transformation of which a few properties are discussed. Exercises are provided at the end of the chapter.

Keywords:   ferromagnetic systems, Legendre transformation, vertex functions, cluster properties

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