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A guide to Monte Carlo simulations in statistical physics /

by Landau, David P [aut]; Binder, K. (Kurt) [aut].
Material type: materialTypeLabelBookPublisher: Cambridge [UK] : Cambridge University Press, 2015Edition: Fourth edition.Description: xvii, 519 p. : ill. ; 26 cm.ISBN: 9781107074026 (hardback).Other title: Monte Carlo simulations in statistical physics.Subject(s): Monte Carlo method | Statistical physics
Contents:
Preface -- 1 Introduction -- 1.1 What is a Monte Carlo simulation -- 1.2 What problems can we solve with it? -- 1.3 What difficulties will we encounter? -- 1.3.1 Limited computer time and memory -- 1.3.2 Statistical and other errors -- 1.4 What strategy should we follw in approaching a problem? -- 1.5 How do simulations relate to theory and experiment? -- 2 Some necessary background -- 2.1 Thermodynamics and statistical mechanics: a quick reminder -- 2.1.1 Basic notions -- 2.1.2 Phase transitions -- 2.1.3 Ergodicity and broken symmetry. 2.1.4 Fluctuations and the Ginzburg criterion -- 2.1.5 A standard exercise: the ferromagnetic Ising model -- 2.2 Probabilty theory -- 2.2.1 Basic notions -- 2.2.2 Special probability distributions and the central limit theorem -- 2.2.3 Statistical errors -- 2.2.4 Markov chains and master equations -- 2.2.5 The 'art' of random number generation -- 2.3 Non-equilibrium and dynamics: some introductory comments -- 2.3.1 Physical applications of master equations -- 2.3.2 Conservation laws and their consequences -- 2.3.3 Critical slowing down at phase transitions -- 2.3.4 Transport coefficients. 2.3.5 Concluding comments: why bother about dynamics whendoing Monte Carlo for statics? -- References -- 3 Simple sampling Monte Carlo methods -- 3.1 Introduction -- 3.2 Comparisons of methods for numerical integration of given functions -- 3.2.1 Simple methods -- 3.2.2 Intelligent methods -- 3.3 Boundary value problems -- 3.4 Simulation of radioactive decay -- 3.5 Simulation of transport properties -- 3.5.1 Neutron support -- 3.5.2 Fluid flow -- 3.6 The percolation problem -- 3.61 Site percolation -- 3.6.2 Cluster counting: the Hoshen-Kopelman alogorithm -- 3.6.3 Other percolation models. 3.7 Finding the groundstate of a Hamiltonian -- 3.8 Generation of 'random' walks -- 3.8.1 Introduction -- 3.8.2 Random walks -- 3.8.3 Self-avoiding walks -- 3.8.4 Growing walks and other models -- 3.9 Final remarks -- References -- 4 Importance sampling Monte Carlo methods -- 4.1 Introduction -- 4.2 The simplest case: single spin-flip sampling for the simple Ising model -- 4.2.1 Algorithm -- 4.2.2 Boundary conditions -- 4.2.3 Finite size effects -- 4.2.4 Finite sampling time effects -- 4.2.5 Critical relaxation -- 4.3 Other discrete variable models. 4.3.1 Ising models with competing interactions -- 4.3.2 q-state Potts models -- 4.3.3 Baxter and Baxter-Wu models -- 4.3.4. Clock models -- 4.3.5 Ising spin glass models -- 4.3.6 Complex fluid models -- 4.4 Spin-exchange sampling -- 4.4.1 Constant magnetization simulations -- 4.4.2 Phase separation -- 4.4.3 Diffusion -- 4.4.4 Hydrodynamic slowing down -- 4.5 Microcanonical methods -- 4.5.1 Demon algorithm -- 4.5.2 Dynamic ensemble -- 4.5.3 Q2R -- 4.6 General remarks, choice of ensemble -- 4.7 Staticsand dynamics of polymer models on lattices -- 4.7.1 Background -- 4.7.2 Fixed length bond methods.
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Includes bibliographical references and index.

Preface -- 1 Introduction -- 1.1 What is a Monte Carlo simulation -- 1.2 What problems can we solve with it? -- 1.3 What difficulties will we encounter? -- 1.3.1 Limited computer time and memory -- 1.3.2 Statistical and other errors -- 1.4 What strategy should we follw in approaching a problem? -- 1.5 How do simulations relate to theory and experiment? -- 2 Some necessary background -- 2.1 Thermodynamics and statistical mechanics: a quick reminder -- 2.1.1 Basic notions -- 2.1.2 Phase transitions -- 2.1.3 Ergodicity and broken symmetry. 2.1.4 Fluctuations and the Ginzburg criterion -- 2.1.5 A standard exercise: the ferromagnetic Ising model -- 2.2 Probabilty theory -- 2.2.1 Basic notions -- 2.2.2 Special probability distributions and the central limit theorem -- 2.2.3 Statistical errors -- 2.2.4 Markov chains and master equations -- 2.2.5 The 'art' of random number generation -- 2.3 Non-equilibrium and dynamics: some introductory comments -- 2.3.1 Physical applications of master equations -- 2.3.2 Conservation laws and their consequences -- 2.3.3 Critical slowing down at phase transitions -- 2.3.4 Transport coefficients. 2.3.5 Concluding comments: why bother about dynamics whendoing Monte Carlo for statics? -- References -- 3 Simple sampling Monte Carlo methods -- 3.1 Introduction -- 3.2 Comparisons of methods for numerical integration of given functions -- 3.2.1 Simple methods -- 3.2.2 Intelligent methods -- 3.3 Boundary value problems -- 3.4 Simulation of radioactive decay -- 3.5 Simulation of transport properties -- 3.5.1 Neutron support -- 3.5.2 Fluid flow -- 3.6 The percolation problem -- 3.61 Site percolation -- 3.6.2 Cluster counting: the Hoshen-Kopelman alogorithm -- 3.6.3 Other percolation models. 3.7 Finding the groundstate of a Hamiltonian -- 3.8 Generation of 'random' walks -- 3.8.1 Introduction -- 3.8.2 Random walks -- 3.8.3 Self-avoiding walks -- 3.8.4 Growing walks and other models -- 3.9 Final remarks -- References -- 4 Importance sampling Monte Carlo methods -- 4.1 Introduction -- 4.2 The simplest case: single spin-flip sampling for the simple Ising model -- 4.2.1 Algorithm -- 4.2.2 Boundary conditions -- 4.2.3 Finite size effects -- 4.2.4 Finite sampling time effects -- 4.2.5 Critical relaxation -- 4.3 Other discrete variable models. 4.3.1 Ising models with competing interactions -- 4.3.2 q-state Potts models -- 4.3.3 Baxter and Baxter-Wu models -- 4.3.4. Clock models -- 4.3.5 Ising spin glass models -- 4.3.6 Complex fluid models -- 4.4 Spin-exchange sampling -- 4.4.1 Constant magnetization simulations -- 4.4.2 Phase separation -- 4.4.3 Diffusion -- 4.4.4 Hydrodynamic slowing down -- 4.5 Microcanonical methods -- 4.5.1 Demon algorithm -- 4.5.2 Dynamic ensemble -- 4.5.3 Q2R -- 4.6 General remarks, choice of ensemble -- 4.7 Staticsand dynamics of polymer models on lattices -- 4.7.1 Background -- 4.7.2 Fixed length bond methods.