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Histogram-free multicanonical Monte Carlo sampling to calculate the density of states

Journal Article · · Computer Physics Communications
 [1];  [2];  [2]
  1. The Univ. of Georgia, Athens, GA (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
+ Show Author Affiliations
Here, 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.
Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
DOE Office of Science; USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1484125
Alternate ID(s):
OSTI ID: 1635830
Journal Information:
Computer Physics Communications, Journal Name: Computer Physics Communications Journal Issue: C Vol. 235; ISSN 0010-4655
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (2)

Estimating the density of states of frustrated spin systems journal July 2019
Estimating the Density of States of Frustrated Spin Systems text January 2018

Figures / Tables (9)

Figure 1(p. 5)figure Figure 1
Figure 2(p. 5)figure Figure 2
Figure 3(p. 6)figure Figure 3
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Figure 6(p. 7)figure Figure 6
Table 1(p. 7)table Table 1
Figure 7(p. 10)figure Figure 7
Figure 8(p. 10)figure Figure 8

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Algorithms
Density of states
Monte Carlo
Statistical mechanics