Introduction to Monte Carlo algorithms
These lectures that I gave in the summer of 1996 at the Beg-Rohu (France) and Budapest summer schools discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple and light-weight fashion. The key-words are Markov chains, sampling, detailed balance, a priori probabilities, rejections, ergodicity, “Faster than the clock algorithms”.
The emphasis is on orientation, which is difficult to obtain (all the mathematics being simple). A firm sense of orientation is essential, because it is easy to lose direction, especially when you venture to leave the well trodden paths established by common usage.
The discussion will remain quite basic (and I hope, readable), but I will make every effort to drive home the essential messages: the crystal-clearness of detailed balance, the main problem with Markov chains, the large extent of algorithmic freedom, both in thermodynamic and dynamic Monte Carlo, and the fundamental differences between the two problems.
KeywordsIsing Model Detailed Balance Monte Carlo Algorithm Acceptance Probability Metropolis Algorithm
Unable to display preview. Download preview PDF.
- Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., Numerical Recipes, 2nd edition, Cambridge University Press (1992).Google Scholar
- acf also: Binder, K., in Monte Carlo Methods in Statistical Physics, edited by K. Binder, 2nd ed. (Springer Verlag, Berlin, 1986, sect 1.3.1).Google Scholar
- Krauth, W., Pluchery, O., J. Phys. A: Math Gen 27, L715 (1994).Google Scholar