Monte Carlo Algorithms

So we have a valid Monte Carlo algorithm if:

• We have a means of generating a new configuration B from a previous configuration A such that the transition probability satisfies detailed balance

• The generation procedure is ergodic, i.e. every configuration can be reached from every other configuration in a finite number of iterations

The Metropolis algorithm satisfies the first criterion for all statistical systems. The second criterion is model dependent, and not always true (e.g. at T=0).