Jump to ContentJump to Main Navigation
Statistical Physics, Optimization, Inference, and Message-Passing AlgorithmsLecture Notes of the Les Houches School of Physics: Special Issue, October 2013$
Users without a subscription are not able to see the full content.

Florent Krzakala, Federico Ricci-Tersenghi, Lenka Zdeborova, Riccardo Zecchina, Eric W. Tramel, and Leticia F. Cugliandolo

Print publication date: 2015

Print ISBN-13: 9780198743736

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198743736.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 04 April 2020

Replica theory and spin glasses

Replica theory and spin glasses

Chapter:
(p.61) 3 Replica theory and spin glasses
Source:
Statistical Physics, Optimization, Inference, and Message-Passing Algorithms
Author(s):

Giorgio Parisi

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198743736.003.0003

This chapter starts with an introduction to the replica method, a standard method in statistical physics, along with a concrete application to the computation of the eigenvalue distribution of random matrices in the Gaussian orthogonal ensemble. The solution of the Sherrington–Kirkpatrick (SK) disordered spin-glass model is then derived, along with the phenomenon of replica symmetry breaking (RSB). The physical meaning of the RSB is explained. The ultrametricity of the space of pure states emerges as a consequence of the hierarchical RSB scheme. Moreover, it is shown how some low-temperature properties of physical observables can be derived by invoking the stochastic stability principle. Some rigorous results on the SK model are described: the existence of the thermodynamic limit, and the proof of the exactness of the hierarchical RSB solution.

Keywords:   replica method, spin-glass, random matrix, stochastic stability, replica symmetry breaking

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .