Monte Carlo Simulation in Statistical Physics: An Introduction (Springer Series in Solid-state Sciences)

The Monte Carlo method is a computer simulation method which uses random numbers to simulate statistical fluctuations. The method is used to model complex systems with many degrees of freedom. Probability distributions for these systems are generated numerically and the method then yields numerically exact information on the models. Such simulations may be used to see how well a model system approximates a real one or to see how valid the assumptions are in an analytical theory. A short and systematic theoretical introduction to the method forms the first part of this book. The second part is a practical guide with plenty of examples and exercises for the student. Problems treated by simple sampling (random and self-avoiding walks, percolation clusters, etc.) and by importance sampling (Ising models etc.) are included, along with such topics as finite-size effects and guidelines for the analysis of Monte Carlo simulations. The two parts together provide an excellent introduction to the theory and practice of Monte Carlo simulations.