## Applications of the Lace Expansion to Statistical-Mechanical Models

*Akira Sakai*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0006
- Subject:
- Mathematics, Probability / Statistics, Analysis

Synergetics is a common feature in interesting statistical-mechanical problems. One of the most important examples of synergetics is the emergence of a second-order phase transition and critical ... More

## The Ising model in two dimensions: summary of results

*Barry M. McCoy*

### in Advanced Statistical Mechanics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes the many results of the exactly solved Ising model in two dimensions at H = 0 including: the partition function, free energy, spontaneous magnetization, the Toeplitz ... More

## FLOWS AND FERROMAGNETS

*Geoffrey Grimmett*

### in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.003.0008
- Subject:
- Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More

## Exact solutions and related topics

*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/9780199577224.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Only a limited number of models of phase transitions and critical phenomena can be solved exactly. These examples nevertheless play important roles in many aspects including the verification of the ... More

## Switching Paths for Ising Models with Long-Range Interaction

*Nicolas Dirr*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0011
- Subject:
- Mathematics, Probability / Statistics, Analysis

The chapter discusses a multiscale model for a two-phases material. The model is a stochastic process on the finest scale. The effective behaviour on larger scales is governed by deterministic ... More

## Interacting systems on networks

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter considers systems of interacting agents placed on networks. The agents — spins, oscillators, interacting individuals, etc. — occupy the nodes of networks and interact with each other ... More

## The Pfaffian solution of the Ising model

*Barry M. McCoy*

### in Advanced Statistical Mechanics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the computation of the partition function of the two-dimensional Ising model in terms of a sum of Pfaffians using a combinatorial approach. This method is extended to derive the ... More

## Implementation of the renormalization group

*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/9780199577224.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Actual computations of fixed points and eigenvalues usually involve approximations, often crude ones, except for a very limited number of simple cases such as the one-dimensional Ising model of the ... More

## Counting, Sampling, and Statistical Physics

*Cristopher Moore and Stephan Mertens*

### in The Nature of Computation

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199233212
- eISBN:
- 9780191775079
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233212.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The objects that are solutions to an NP-complete problem are difficult to count. Counting can be a subtle and complex problem even when the corresponding existence and optimisation problems are in P. ... More

## Introduction: The simplest models of magnetism

*Ralph Skomski*

### in Simple Models of Magnetism

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780198570752
- eISBN:
- 9780191718816
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570752.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

During the last 100 years, magnetism has made a giant step forward. However, many questions remained unanswered or were not even asked at that time. What is the atomic origin of the magnetisation, ... More

## Mean-Field Theory of Phase Transitions

*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/9780198509417.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Methods of statistical mechanics have been enormously successful in clarifying the macroscopic properties of many-body systems. Typical examples are found in magnetic systems, which have been a test ... More

## Phase Transitions and the Ising Model

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.003.0030
- Subject:
- Physics, Condensed Matter Physics / Materials

The Ising model provides an extremely useful example for the investigation of phase transitions. This chapter provides both an introduction to the properties of the Ising model and an overview of the ... More

## Statistical Theory, Soft Modes, And Phase Transitions

*M. E. LINES and A. M. GLASS*

### in Principles and Applications of Ferroelectrics and Related Materials

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials

In order to acquire a simple physical picture of the dynamic mechanism of a phase transition it is necessary to use the simplest of many-body approximations. It is instructive, in particular, to ... More

## Duality in generalized Ising models

*Franz J. Wegner*

### in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785781
- eISBN:
- 9780191827600
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785781.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials

These lecture notes deal with Ising models with interactions containing products of more than two spins. After a number of examples have been given, some general statements are presented. Of ... More

## Correlations and creating short‐range order

*Reinhard B. Neder and Thomas Proffen*

### in Diffuse Scattering and Defect Structure Simulations: A cook book using the program DISCUS

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0005
- Subject:
- Physics, Crystallography

This chapter deals with the simulation of short range ordered crystals. Correlations are introduced as a convenient way to describe short-range order (SRO). The most common way to create structures ... More

## Classical spin systems

*Joseph F. Boudreau and Eric S. Swanson*

### in Applied Computational Physics

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is ... More

## Further Issues

*Paul Humphreys*

### in Extending Ourselves: Computational Science, Empiricism, and Scientific Method

- Published in print:
- 2004
- Published Online:
- February 2006
- ISBN:
- 9780195158700
- eISBN:
- 9780199785964
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195158709.003.0005
- Subject:
- Philosophy, Philosophy of Science

Various underdetermination arguments against selective realism are explored and rebutted. The role of abstraction and idealization in templates is explored. The fact that most computational processes ... More

## Phase Transitions and the Ising Model

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2019
- Published Online:
- February 2020
- ISBN:
- 9780198853237
- eISBN:
- 9780191887703
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853237.003.0031
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution ... More

## Phase transitions and their devices

*Sandip Tiwari*

### in Nanoscale Device Physics: Science and Engineering Fundamentals

- Published in print:
- 2017
- Published Online:
- August 2017
- ISBN:
- 9780198759874
- eISBN:
- 9780191820847
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198759874.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

Phase transitions as a collective response of an ensemble, with appearance of unique stable properties spontaneously, is critical to a variety of devices: electronic, magnetic, optical, and their ... More

## New Tools for Extreme-Value Analysis: Statistical Physics Goes beyond Its Borders

*Franck Jovanovic and Christophe Schinckus*

### in Econophysics and Financial Economics: An Emerging Dialogue

- Published in print:
- 2017
- Published Online:
- December 2016
- ISBN:
- 9780190205034
- eISBN:
- 9780190205065
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190205034.003.0003
- Subject:
- Economics and Finance, Financial Economics

Chapter 3 clarifies the theoretical and methodological foundations of econophysics. This crucial chapter details the contextual factors that contributed to the advent of econophysics. More precisely, ... More