The Metropolis algorithm , see the original article (see also the FYS3150 lectures) was invented by Metropolis et. al and is often simply called the Metropolis algorithm. It is a method to sample a normalized probability distribution by a stochastic process. We define \( {\cal P}_i^{(n)} \) to be the probability for finding the system in the state \( i \) at step \( n \). The algorithm is then

• Sample a possible new state \( j \) with some probability \( T_{i\rightarrow j} \).
• Accept the new state \( j \) with probability \( A_{i \rightarrow j} \) and use it as the next sample. With probability \( 1-A_{i\rightarrow j} \) the move is rejected and the original state \( i \) is used again as a sample.