Statistical mechanics : algorithms and computations / Werner Krauth.

Format:

Book

Author/Creator:

Krauth, Werner, author.

Series:

Oxford master series in physics.

Oxford master series in statistical, computational, and theoretical physics.

Oxford scholarship online.

Oxford master series in physics

Oxford master series in statistical, computational, and theoretical physics

Oxford scholarship online

Language:

English

Subjects (All):

Statistical mechanics.

Statistical mechanics--Problems, exercises, etc.

Statistical physics.

Statistical physics--Problems, excercises, etc.

Physical Description:

xii, 342 p. : ill.

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

Containing many illustrations, tables & printed algorithms, this book discusses the computational approach in modern statistical physics. Offering a discussion of key subjects in classical and quantum statistical physics, it is intended for students, teachers & researchers in physics & related sciences.

Contents:

Intro

Contents

1 Monte Carlo methods

1.1 Popular games in Monaco

1.1.1 Direct sampling

1.1.2 Markov-chain sampling

1.1.3 Historical origins

1.1.4 Detailed balance

1.1.5 The Metropolis algorithm

1.1.6 A priori probabilities, triangle algorithm

1.1.7 Perfect sampling with Markov chains

1.2 Basic sampling

1.2.1 Real random numbers

1.2.2 Random integers, permutations, and combinations

1.2.3 Finite distributions

1.2.4 Continuous distributions and sample transformation

1.2.5 Gaussians

1.2.6 Random points in/on a sphere

1.3 Statistical data analysis

1.3.1 Sum of random variables, convolution

1.3.2 Mean value and variance

1.3.3 The central limit theorem

1.3.4 Data analysis for independent variables

1.3.5 Error estimates for Markov chains

1.4 Computing

1.4.1 Ergodicity

1.4.2 Importance sampling

1.4.3 Monte Carlo quality control

1.4.4 Stable distributions

1.4.5 Minimum number of samples

Exercises

References

2 Hard disks and spheres

2.1 Newtonian deterministic mechanics

2.1.1 Pair collisions and wall collisions

2.1.2 Chaotic dynamics

2.1.3 Observables

2.1.4 Periodic boundary conditions

2.2 Boltzmann's statistical mechanics

2.2.1 Direct disk sampling

2.2.2 Partition function for hard disks

2.2.3 Markov-chain hard-sphere algorithm

2.2.4 Velocities: the Maxwell distribution

2.2.5 Hydrodynamics: long-time tails

2.3 Pressure and the Boltzmann distribution

2.3.1 Bath-and-plate system

2.3.2 Piston-and-plate system

2.3.3 Ideal gas at constant pressure

2.3.4 Constant-pressure simulation of hard spheres

2.4 Large hard-sphere systems

2.4.1 Grid/cell schemes

2.4.2 Liquid-solid transitions

2.5 Cluster algorithms

2.5.1 Avalanches and independent sets

2.5.2 Hard-sphere cluster algorithm

References.

3 Density matrices and path integrals

3.1 Density matrices

3.1.1 The quantum harmonic oscillator

3.1.2 Free density matrix

3.1.3 Density matrices for a box

3.1.4 Density matrix in a rotating box

3.2 Matrix squaring

3.2.1 High-temperature limit, convolution

3.2.2 Harmonic oscillator (exact solution)

3.2.3 Infinitesimal matrix products

3.3 The Feynman path integral

3.3.1 Naive path sampling

3.3.2 Direct path sampling and the Lévy construction

3.3.3 Periodic boundary conditions, paths in a box

3.4 Pairdensity matrices

3.4.1 Two quantum hard spheres

3.4.2 Perfect pair action

3.4.3 Many-particle density matrix

3.5 Geometry of paths

3.5.1 Paths in Fourier space

3.5.2 Pathmaxima, correlation functions

3.5.3 Classical random paths

4 Bosons

4.1 Ideal bosons (energy levels)

4.1.1 Single-particle density of states

4.1.2 Trapped bosons (canonical ensemble)

4.1.3 Trapped bosons (grand canonical ensemble)

4.1.4 Large-N limit in the grand canonical ensemble

4.1.5 Differences between ensembles-.uctuations

4.1.6 Homogeneous Bose gas

4.2 The ideal Bose gas (density matrices)

4.2.1 Bosonic density matrix

4.2.2 Recursive counting of permutations

4.2.3 Canonical partition function of ideal bosons

4.2.4 Cycle-length distribution, condensate fraction

4.2.5 Direct-sampling algorithm for ideal bosons

4.2.6 Homogeneous Bose gas, winding numbers

4.2.7 Interacting bosons

5 Order and disorder in spin systems

5.1 The Ising model-exact computations

5.1.1 Listing spin configurations

5.1.2 Thermodynamics, specific heat capacity, and magnetization

5.1.3 Listing loop configurations

5.1.4 Counting (not listing) loops in two dimensions

5.1.5 Density of states from thermodynamics.

5.2 The Ising model-Monte Carlo algorithms

5.2.1 Local sampling methods

5.2.2 Heat bath and perfect sampling

5.2.3 Cluster algorithms

5.3 Generalized Ising models

5.3.1 The two-dimensional spin glass

5.3.2 Liquids as Ising-spin-glass models

6 Entropic forces

6.1 Entropic continuum models and mixtures

6.1.1 Random clothes-pins

6.1.2 The Asakura-Oosawa depletion interaction

6.1.3 Binary mixtures

6.2 Entropic lattice model: dimers

6.2.1 Basic enumeration

6.2.2 Breadth-.rst and depth-first enumeration

6.2.3 Pfaffian dimer enumerations

6.2.4 Monte Carlo algorithms for the monomer-dimer problem

6.2.5 Monomer-dimer partition function

7 Dynamic Monte Carlo methods

7.1 Random sequential deposition

7.1.1 Faster-than-the-clock algorithms

7.2 Dynamic spin algorithms

7.2.1 Spin-flips and dice throws

7.2.2 Accelerated algorithms for discrete systems

7.2.3 Futility

7.3 Disks on the unit sphere

7.3.1 Simulated annealing

7.3.2 Asymptotic densities and paper-cutting

7.3.3 Polydisperse disks and the glass transition

7.3.4 Jamming and planar graphs

Acknowledgements

Index.

Notes:

Formerly CIP.

Previously issued in print: 2006.

Includes bibliographical references and index.

Derived record based on print version record and publisher information.

Description based on publisher supplied metadata and other sources.

ISBN:

1-383-02272-0

1-280-75240-8

1-4294-5950-6

0-19-152332-1

OCLC:

437115734