A guide to Monte Carlo simulations in statistical physics

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

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Bibliographic Details
Main Author: Landau, David P.
Other Authors: Binder, K. (Kurt), 1944-
Format: eBook
Language:English
Published: Cambridge ; New York : Cambridge University Press, 2000.
Subjects:
Monte Carlo method.
Statistical physics.
SCIENCE > Physics > General.
Monte Carlo method
Statistical physics
Monte Carlo-methode.
Statistische mechanica.
Simulatie.
MÉTODO DE MONTE CARLO.
MECÂNICA ESTATÍSTICA.
Online Access:Click for online access
Table of 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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