Transition Matrix Monte Carlo

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...

Convergence Analysis of Markov Chain Monte Carlo Linear Solvers Using Ulam-von Neumann Algorithm

The convergence of Markov chain–based Monte Carlo linear solvers using the Ulam– von Neumann algorithm for a linear system of the form x = Hx + b is investigated in this paper. We analyze the convergence of the Monte Carlo solver based on the original Ulam–von Neumann algorithm under the conditions that ‖H‖ < 1 as well as ρ(H) < 1, where ρ(H) is the spectral radius of H. We find that although t...

Flat histogram Monte Carlo method

We discuss a sampling algorithm which generates flat histogram in energy. In combination with transition matrix Monte Carlo, the density of states and derived quantities such as entropy and free energy as a function of temperature can be computed in a single simulation.

Transition matrix Monte Carlo and flat-histogram algorithm

In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can be calculated, including free energy and entropy. We discuss single-spin-flip algorithms, such as flat-histogram and equal-hit algorithms, that can be used ...

On the Optimal Transition Matrix for Markov Chain Monte Carlo Sampling