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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


Statistical Physics of Spin Glasses and Information Processing: An Introduction

Hidetoshi Nishimori

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical ... More


Mathematics and Physics: Strategies of Assimilation

Alasdair Urquhart

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0017
Subject:
Philosophy, Logic/Philosophy of Mathematics

The main topic of this chapter is the problem posed to the mathematical community by the non-rigorous methods used by physicists in investigating mathematical problems. These methods are often highly ... More


Mean-Field Theory of Spin Glasses

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/9780198509417.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Error-Correcting Codes

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/9780198509417.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Reliable transmission of information through noisy channels plays a vital role in modern society. Some aspects of this problem have close formal similarities to the theory of spin glasses. Noise in ... More


Random systems

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Real materials always contain randomness or disorder that cannot be expressed by idealized simple model systems. The present chapter studies the effects of randomness on phase transitions and ... More


Optimization Problems

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/9780198509417.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A decision-making problem is often formulated as the minimization or maximization of a multivariable function, an optimization problem. This chapter shows that the methods of statistical mechanics ... 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


Minority game

František Slanina

in Essentials of Econophysics Modelling

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199299683
eISBN:
9780191747038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199299683.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter we present the minority game, which is one of the keystone models of econophysics. It is the mathematic implementation of the idea of inductive, rather than deductive, thinking. ... 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


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

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

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book contains a collection of the presentations that were given in October 2013 at the Les Houches Autumn School on statistical physics, optimization, inference, and message-passing algorithms. ... More


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