## Advanced Statistical Mechanics

*Barry M McCoy*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ... More

## The symmetric group Sr and Young tableaux

*Adam M. Bincer*

### in Lie Groups and Lie Algebras: A Physicist's Perspective

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199662920
- eISBN:
- 9780191745492
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662920.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The symmetric group Sr and Young tableaux are defined. It is shown that the actions of the symmetric group and unitary group commute, therefore SU(n) tensors can be classified by ... More

## Number partitioning

*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/9780198570837.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Number partitioning is one of the most basic optimization problems. It is very easy to state: ‘Given the values of N assets, is there a fair partition of them into two sets?’ Nevertheless, it is very ... More

## Basic principles

*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/9780199556632.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic results of thermodynamics. It derives the basic formulas of the canonical and grand canonical ensemble from the microcanonical ensemble. It defines the concept of a ... 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

## 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

## Dynamical Entropy

*Robert Alicki and Mark Fannes*

### in Quantum Dynamical Systems

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in ... More

## PATH INTEGRALS IN QUANTUM MECHANICS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs the path integral associated with the statistical operator e -βH in the case of Hamiltonians of the simple form p2/2m + V (q). The path ... More

## PARTITION FUNCTION AND SPECTRUM

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

A direct application of the calculation of the partition function is provided by determining the spectrum of a Hamiltonian (which is assumed to be discrete, for simplicity). In this chapter, only ... More

## CLASSICAL AND QUANTUM STATISTICAL PHYSICS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter provides a simple physical interpretation to the formal continuum limit that has led, from an integral over position variables corresponding to discrete times, to a path integral. It ... More

## PATH INTEGRALS AND HOLOMORPHIC FORMALISM

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0006
- Subject:

This chapter introduces the holomorphic representation of quantum mechanics, because it allows a study of the properties of boson systems both from the point of view of evolution and of quantum ... More

## PATH INTEGRALS: FERMIONS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0007
- Subject:

The methods that have been described in previous chapters can be used to study general quantum Bose systems. They are based in a direct way on the introduction of a generating function of symmetric ... 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

## Approaches to non‐equilibrium economics

*Peter Richmond, Jürgen Mimkes, and Stefan Hutzler*

### in Econophysics and Physical Economics

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199674701
- eISBN:
- 9780191780066
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199674701.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter shows that, in economics, a statistical mechanics in which the allowable states of the system are associated with a constant dither, leading to free energies that are proportional to the ... More

## Accounting for all parts (subgraphs)

*Ernesto Estrada*

### in The Structure of Complex Networks: Theory and Applications

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199591756
- eISBN:
- 9780191774959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199591756.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the concept of invariants aimed at characterising the global subgraph structure of a network. The discussions cover functions of adjacency matrix, such as the Estrada index; the ... More

## Community structure of networks

*Ernesto Estrada*

### in The Structure of Complex Networks: Theory and Applications

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199591756
- eISBN:
- 9780191774959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199591756.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the methods currently used for detecting network communities. It starts with an intuitive introduction of the concept of network community. The chapter then considers methods ... More

## Equilibrium Statistical Mechanics

*Hans-Peter Eckle*

### in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 4 reviews the basic notions of equilibrium statistical mechanics and begins with its fundamental postulate and outlines the structure of the theory using the most important of the various ... More

## Simple Systems

*Jochen Rau*

### in Statistical Physics and Thermodynamics: An Introduction to Key Concepts

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199595068
- eISBN:
- 9780191844300
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199595068.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic ... More

## Refining the Definition of Entropy

*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/9780198853237.003.0021
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

If a macroscopic system as ever been in thermal contact with another macroscopic system, the width of the energy distribution is not zero. This is in contrast to the approximation made in Chapter 7 ... More

## Ensembles with hard constraints

*A.C.C. Coolen, A. Annibale, and E.S. Roberts*

### in Generating Random Networks and Graphs

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198709893
- eISBN:
- 9780191780172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198709893.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces random graph ensembles involving hard constraints such as setting a fixed total number of links or fixed degree sequence, including properties of the partition function. It ... More