Introduction To Monte Carlo Algorithms

Details Introduction To Monte Carlo Algorithms Introduction To Monte Carlo Algorithms

1996-12-20

arxiv.org/abs/cond-mat/9612186v2

in 'Advances in Computer Simulation' J. Kertesz and I. Kondor, eds, Lecture Notes in Physics (Springer Verlag, 1998)

Physics

Condensed Matter

Statistical Mechanics

43 pages, many figures, 5 original drawings by the author, Latex

Scientific paper

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 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.

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