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The Infinite-Range Spin Glass

Daniel L. Stein and Charles M. Newman

in Spin Glasses and Complexity

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691147338
eISBN:
9781400845637
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147338.003.0006
Subject:
Sociology, Science, Technology and Environment

This chapter introduces mean field theory, both as a general class of models and in its specific incarnation in spin glasses, the Sherrington–Kirkpatrick model. This is undoubtedly the most ... More


Introduction to replica theory

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Replica Symmetry Breaking

Hidetoshi Nishimori

in Statistical Physics of Spin Glasses and Information Processing: An Introduction

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Disordered ultracold atomic gases

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as ... More


Replica theory and spin glasses

Giorgio Parisi

in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


The 1RSB cavity method

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In graphical models whose factor graph has a locally tree-like structure, belief propagation may fail because variables become correlated at large distances. This phenomenon has been observed in many ... More


An ongoing story

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0022
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The emerging field that has been described in this book is remarkably coherent, but it also opens up a number of challenges. This chapter provides a synthetic description of such challenges, as well ... More


Cavity method: message-passing from a physics perspective

Marc Mézard

in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The cavity method is introduced as a heuristic framework from a physics perspective to solve probabilistic graphical models and is presented at both the replica symmetry (RS) and one-step replica ... More


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