Properties of parallel Wang-Landau algorithm with transition matrix control

2023. No. ssrn.4497091.

Fadeeva Marina, Shchur L.

We apply a transition matrix in the energy spectrum to analyze the flatness criteria in each energy window of parallel implementation of the Wang-Landau algorithm. The tunneling time of a random walker in each window does depend on the position of the window in the energy spectrum and is much less than the tunneling time of the entire spectrum. Therefore the parallel Wang-Landau algorithm should be more efficient for larger system sizes. We replace the flatness criterion with the criterion of proximity of the transition matrixes to stochastic ones. A detailed analysis was carried out on the example of the Ising model.

Keywords: матрица переходов, density of states, плотность состояний, Wang-Landau algorithm, алгоритм Ванга-Ландау, Transition matrix in energy space, Stochastic matrix, стохастическая матрица

Publication based on the results of: Computer modeling and machine learning of actual problems of physics (2024)