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.