Introduction To Monte Carlo Algorithms

In these lectures, given in ’96 summer schools in Beg-Rohu (France) and Budapest, I discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple light-weight fashion. The keywords 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 helps to avoid getting lost, especially if you want to leave safe trodden-out paths established by common usage. Even though I will remain quite basic (and, I hope, readable), I make every effort to drive home the essential messages, which are easily explained: the crystal-clearness of detail balance, the main problem with Markov chains, the great algorithmic freedom, both in thermodynamic and dynamic Monte Carlo, and the fundamental differences between the two problems.