  We report a new multicanonical Monte Carlo algorithm to obtain the density of
states for physical systems with continuous state variables in statistical
mechanics. Our algorithm is able to obtain a closed-form expression for the
density of states expressed in a chosen basis set, instead of a numerical array
of finite resolution as in previous variants of this class of MC methods such
as the multicanonical sampling and Wang-Landau sampling. This is enabled by
storing the visited states directly and avoiding the explicit collection of a
histogram. This practice also has the advantage of avoiding undesirable
artificial errors caused by the discretization and binning of continuous state
variables. Our results show that this scheme is capable of obtaining converged
results with a much reduced number of Monte Carlo steps, leading to a
significant speedup over existing algorithms.
