Transition Matrix Monte Carlo Method
نویسندگان
چکیده
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.
منابع مشابه
Transition Matrix Monte Carlo
Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from independent simulations. In this paper, we describe an complementary approach to extracting information from Monte Carlo simulations that uses the matrix of transition...
متن کاملFlat 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.
متن کاملTransition 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 ...
متن کاملConvergence 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...
متن کاملEfficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations
An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical er...
متن کامل