Optimal Modification Factor and Convergence of the Wang-Landau Algorithm

Abstract

We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e. the statistical error vanishes as $1/\sqrt{t}$, where $t$ is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than $1/t$. Our findings are consistent with the $1/t$ Wang-Landau algorithm discovered recently, and we argue that one needs external information in the simulation to beat the conventional Monte Carlo algorithm.

19 pages and 3 figures, to be published in Phys. Rev. E

References in corpus (3)

• Equilibrium free energies from non-equilibrium metadynamics
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling