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A histogram-free multicanonical Monte Carlo algorithm for the construction of analytical density of states...

by Ying Wai Li, Markus Eisenbach
Publication Type
Conference Paper
Book Title
PASC '17 Proceedings of the Platform for Advanced Scientific Computing Conference
Publication Date
Publisher Location
New York, New York, United States of America
Conference Name
The Platform for Advanced Scientific Computing Conference (PASC17)
Conference Location
Lugano, Switzerland
Conference Date
-

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS 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 (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set 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.