Transition Matrix Monte Carlo Method

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods. PACS numbers: 02.70.Tt, 05.10.Ln, 05.50.+q. Keywords: Monte Carlo method, flat histogram, multi-canonical ensemble.