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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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Replica Symmetry Breaking

Replica Symmetry Breaking

(p.23) 3 Replica Symmetry Breaking
Statistical Physics of Spin Glasses and Information Processing

Hidetoshi Nishimori

Oxford University Press

This chapter continues the analysis of the Sherrington–Kirkpatrick (SK) model started in the preceding chapter. The free energy of the SK model derived under the ansatz of replica symmetry has the problem of negative entropy at low temperatures. It is therefore natural to investigate the possibility that the order parameter may assume various values depending upon the replica indices. The theory of replica symmetry breaking started in this way as a mathematical effort to avoid unphysical conclusions of the replica-symmetric solution. It turned out, however, that the scheme of replica symmetry breaking developed by Parisi has a very rich physical implication, namely the existence of a vast variety of stable states with ultrametric structure in the phase space. The chapter is devoted to the elucidation of this story.

Keywords:   SK model, replica symmetry breaking, Parisi solution, ultrametricity, negative entropy

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