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## Mean‐field theories

*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/9780199577224.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The present chapter explains the mean-field approximation, the Landau theory, the infinite-range model, and the Bethe approximation, and shows that all these (mean-field) theories are essentially ... More

## Renormalization group and scaling

*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/9780199577224.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary ... More

## Critical phenomena and scaling theory

*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/9780199556632.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the phenomenological description of critical phenomena. It derives inequalities for critical exponents which follow from thermodynamics. It explains the scaling theory of ... More

## High temperature expansions for magnets at H = 0

*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/9780199556632.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this ... More

## Spontaneous time‐symmetry breaking in a vibrating cold atom system

*M.-S. Heo, Y. Kim, H.-R. Noh, and W. Jhe*

### in Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199691388
- eISBN:
- 9780191742255
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691388.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the experimental and theoretical studies of a spontaneous time-translation symmetry breaking transition in a non-equilibrium cold atom system. Such studies prepare two ... More

## Quantum phase transitions

*G. G. Batrouni and R. T. Scalettar*

### in Ultracold Gases and Quantum Information: Lecture Notes of the Les Houches Summer School in Singapore: Volume 91, July 2009

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199603657
- eISBN:
- 9780191729515
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199603657.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses quantum phase transitions (QPT). It starts with a brief review of thermal phase transitions, critical exponents and scaling laws. The scaling laws are then generalized to the ... More

## Field theory: Perturbative expansion and summation methods

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0023
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 23 examines perturbative expansion and summation methods in field theory. In quantum field theory, all perturbative expansions are divergent series in the mathematical sense. This leads to a ... More

## Renormalization Group: From a general concept to numbers

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples ... More

## Continuous phase transitions

*Andrew M. Steane*

### in Thermodynamics: A complete undergraduate course

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198788560
- eISBN:
- 9780191830426
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198788560.003.0025
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The general phenomenon of continuous phase transitions is discussed, and treated by the Landau mean field approach. First some illustrative examples are discussed, and the concepts of order parameter ... 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

## Ferromagnetism: a renormalization group tutorial

*Tom Lancaster and Stephen J. Blundell*

### in Quantum Field Theory for the Gifted Amateur

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0036
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter treats the ferromagnetic transition as a further example of the renormalization group procedure and shows how critical exponents can be extracted.

## Magnetic Materials: From Isolated Moments to Ordered Arrangements

*Kannan M. Krishnan*

### in Fundamentals and Applications of Magnetic Materials

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780199570447
- eISBN:
- 9780191813504
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570447.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

The magnetic behavior of materials can be quite diverse with a wide range of susceptibilities. All materials exhibit diamagnetism with a very small, negative susceptibility and it is predominant in ... More

## Thermodynamic Scaling Near the Critical Point

*Eldred H. Chimowitz*

### in Introduction to Critical Phenomena in Fluids

- Published in print:
- 2005
- Published Online:
- November 2020
- ISBN:
- 9780195119305
- eISBN:
- 9780197561249
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195119305.003.0005
- Subject:
- Chemistry, Physical Chemistry

Thermodynamic scaling near the critical point is a signature of critical phenomena, and many useful applications of supercritical solvent fluids depend upon exploiting ... More

## The Phase Transition in the Random HornSAT Problem

*Demetrios D. Demopoulos and Moshe Y. Vardi*

### 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/9780195177374.003.0017
- Subject:
- Computer Science, Mathematical Theory of Computation

This chapter presents a study of the satisfiability of random Horn formulas and a search for a phase transition. In the past decade, phase transitions or ... More

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