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We report a new multicanonical Monte Carlo (MC) algorithm to obtain thedensity of states (DOS) for physical systems with continuous state variables instatistical mechanics. Our algorithm is able to obtain an analytical form forthe DOS expressed in a chosen basis set, instead of a numerical array of finiteresolution as in previous variants of this class of MC methods such as themulticanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabledby storing the visited states directly in a data set and avoiding the explicitcollection of a histogram. This practice also has the advantage of avoidingundesirable artificial errors caused by the discretization and binning ofcontinuous state variables. Our results show that this scheme is capable ofobtaining converged results with a much reduced number of Monte Carlo steps,leading to a significant speedup over existing algorithms.

A histogram-free multicanonical Monte Carlo algorithm for the basis expansion of density of states