A guide to Monte Carlo simulations in statistical physics / David P. Landau, Kurt Binder.

Includes bibliographical references and index.

Print version record.

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.

This book deals with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics as well as in related fields, for example polymer science and lattice gauge theory. After briefly recalling essential background in statistical mechanics and probability theory, the authors give a succinct overview of simple sampling methods. The next several chapters develop the importance sampling method. The concepts behind the various simulation algorithms are explained. The fact that simulations deal with small systems is emphasized. Othe.

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