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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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Introduction to replica theory

Introduction to replica theory

(p.145) 8 Introduction to replica theory
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

In the past twenty-five years, the replica method has evolved into a rather sophisticated tool for attacking theoretical problems as diverse as spin glasses, protein folding, vortices in superconductors, combinatorial optimization, etc. Although it is not be the main tool of this book, it is nevertheless instructive to have some knowledge of replicas: the replica method is a non-trivial construction which is surprisingly powerful. Several of its most important predictions have been confirmed rigorously through alternative approaches. This chapter gives a compact account of the replica method. It describes the close connection between replica symmetry breaking and the Poisson–Dirichlet process, and it emphasizes the role played by ‘overlaps’ between replicas.

Keywords:   replica method, overlap, replica symmetry breaking, Poisson–Dirichlet process, spin glass, superconductors

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