Statistical Physics @ Trieste

Course: Monte Carlo Methods by Mauro Sellitto

4-state Potts model;re

The objective of this Course is to provide an introduction to Monte Carlo methods, which are probabilistic computational techniques with a wide and growing range of applications.
Prerequisites: Students should be familiar with basic probability and, for practical applications, programming.

Main topics

1. Randomized vs Deterministic Algorithms: The curse of dimensionality.
- Uniform, Importance and Rejection Sampling
2. Markov Chain Monte Carlo
- Metropolis and heat-bath algorithms
3. Dynamical slowing down
- Cluster and faster than the clock algorithms
4. Exact sampling
- Coupling from the past
5. Frustration and optimization
- Annealing and Tempering
6. Dynamically arrested states
- Sampling blocked configurations
7. Non-equilibrium steady states
- Direct evaluation of large-deviations function
References
- W. Krauth, Statistical Mechanics: Algorithms and Computations (Oxford University Press, 2006). See also http://xxx.lanl.gov/pdf/cond-mat/9612186
- D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms (Cambridge University Press, 2005, 4th Ed.), Chaps. 29-32. See http://www.inference.phy.cam.ac.uk/mackay/itila/book.html
- P. Young, Monte Carlo Simulations in Statistical Physics, http://physics.ucsc.edu/~peter/converge_new.pdf
- S.K. Ma, Statistical Mechanics (Singapore: World Scientific, 1985), Chap. 25
- M. Jerrum and A. Sinclair, Markov Chain Monte Carlo Method: an approach to approximate counting and integration. See http://www.cs.berkeley.edu/~sinclair/mcmc.ps