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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

## 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

## 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

## 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

## The Satisfiability Threshold Conjecture: Techniques Behind Upper Bound Improvements

*Lefteris M. Kirousis and Lefteris M. Stamatiou*

### in Computational Complexity and Statistical Physics

- Published in print:
- 2005
- Published Online:
- November 2020
- ISBN:
- 9780195177374
- eISBN:
- 9780197562260
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195177374.003.0015
- Subject:
- Computer Science, Mathematical Theory of Computation

One of the most challenging problems in probability and complexity theory is to establish and determine the satisfiability threshold, or phase transition, for random 3-SAT instances: Boolean ... More

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