Statistical Mechanics: Algorithm and Computations

Chapter 1: Monte Carlo Methods

• we set out to study a host of classical and quantum problems, all of value as models and with numerous applications and generalizations
• we also discuss the basic principles of statistical data analysis: how to extract results from well-behaved simulations
• Monte carlos is extremely general, and the basic recipes allow us - in principle - to solve any problem in statistical physics
• in practice, much effort has to be spent in designing algorithms specifically geared to the problem at hand
• concept of sampling
  • 2 fundamentally different sampling approaches: direct sampling and
  • markov-chain sampling: requires Metropolis algorithm
• Monte Carlo method is a powerful approach for the calculation of integrals