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Statistical Physics of Spin Glasses and Information ProcessingAn Introduction$
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Hidetoshi Nishimori

Print publication date: 2001

Print ISBN-13: 9780198509417

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509417.001.0001

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Mean-Field Theory of Spin Glasses

Mean-Field Theory of Spin Glasses

Chapter:
(p.11) 2 Mean-Field Theory of Spin Glasses
Source:
Statistical Physics of Spin Glasses and Information Processing
Author(s):

Hidetoshi Nishimori

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509417.003.0002

This chapter discusses the problem of spin glasses. If the interactions between spins are not uniform in space, the analysis of the previous chapter does not apply. In particular, when the interactions are ferromagnetic for some bonds and antiferromagnetic for others, the spin orientation cannot be uniform in space, unlike the ferromagnetic system. Under such a circumstance it sometimes happens that spins become randomly frozen — random in space but frozen in time. This is the intuitive picture of the spin glass phase. The chapter investigates the condition for the existence of the spin glass phase as an extension of the mean-field theory. In particular, the properties of the so-called replica-symmetric solution are explained in detail for the Sherrington–Kirkpatrick (SK) model.

Keywords:   Sherrington–Kirkpatrick model, mean-field theory, replica method, replica-symmetric solution, random freezing, non-uniform ordering

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