文档介绍：arXiv:cond-mat/9612186 v1 20 Dec 1996
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nrdcinT ot al Algorithms Carlo Monte To Introduction
NSLbrtied hsqeStatistique Physique RS-Laboratoire
-53 ai ee 5 France 05, Cedex Paris F-75231
cl oml Sup´erieure Normale Ecole
enrKrauth Werner
coe ,2002 2, October
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Abstract
In these lectures, given in ’96 summer schools in Beg-Rohu (France) and
Budapest, I discuss the fundamental principles of thermodynamic and dy-
namic Monte Carlo methods in a simple 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 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.
Chapter 1
Equilibrium Monte Carlo
methods
A Game in Monaco
The word “Monte Carlo method” can be traced back to a game very popular
in Monaco. It’s not what you think, it’s mostly a children’s pass-time played
on the beaches. On Wednesdays (when there is no school) and on weekends,
they get together, pick up a big stick, draw a circle and a square as shown in
figure . They fill their pockets with pebbles 1. Then they stand around,
Figure : Children at play on the beaches of Monaco. They spend their
afternoons calculating π by a method which can be easily extended to general
integrals.
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close their eyes, and throw the pebbles randomly in the direction of the