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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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Scaling Behaviour In The Critical Domain

Scaling Behaviour In The Critical Domain

Chapter:
(p.636) 26 SCALING BEHAVIOUR IN THE CRITICAL DOMAIN
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0026

Chapter 25 established the scaling behaviour of correlation functions at criticality, T = Tc . This chapter studies the critical domain which is defined by the property that the correlation length is large with respect to the microscopic scale, but finite. Using results proven in Chapter 10, it first demonstrates strong scaling above Tc : in the critical domain above Tc , all correlation functions, after rescaling, can be expressed in terms of universal correlation functions, in which the scale of distance is provided by the correlation length. The first part of the chapter is restricted to Ising-like systems. It then generalizes the results to N-component order parameters in Section 26.6. In Section 26.7, shows how to expand the universal two-point function when T approaches Tc , using the short distance expansion. Finally, the appendix discusses the energy correlation function when the specific heat exponent vanishes.

Keywords:   correlation functions, Ising-like systems, energy correlation, specific heat exponent

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