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We report a new multicanonical Monte Carlo algorithm to obtain the density ofstates for physical systems with continuous state variables in statisticalmechanics. Our algorithm is able to obtain a closed-form expression for thedensity of states expressed in a chosen basis set, instead of a numerical arrayof finite resolution as in previous variants of this class of MC methods suchas the multicanonical sampling and Wang-Landau sampling. This is enabled bystoring the visited states directly and avoiding the explicit collection of ahistogram. This practice also has the advantage of avoiding undesirableartificial errors caused by the discretization and binning of continuous statevariables. Our results show that this scheme is capable of obtaining convergedresults with a much reduced number of Monte Carlo steps, leading to asignificant speedup over existing algorithms.

Histogram-Free Multicanonical Monte Carlo Sampling to Calculate the Density of States