Stochastic Approximation Monte Carlo with a Dynamic Update Factor

We present a new Monte-Carlo algorithm based on the Stochastic Approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is Stochastic Approximation with a Dynamic update factor (SAD) which dynamically adjusts the update factor $\gamma$ during the course of the simulation. We test this method on the square-well fluid and compare the convergence time and average entropy error for several related Monte-Carlo methods. We find that both the SAD and $1/t$-Wang-Landau ($1/t$-WL) methods rapidly converge to the correct density of states without the need for the user to specify an arbitrary tunable parameter $t_0$ as in the case of SAMC. SAD requires as input the temperature range of interst, in contrast to $1/t$-WL, which requires that the user identify the interesting range of energies. Thus SAD is more convenient when the range of energies is not known in advance.