Stochastic approximation Monte Carlo with a dynamic update factor

Jordan K. Pommerenck, Tanner T. Simpson, Michael A. Perlin, and David Roundy
Phys. Rev. E 101, 013301 – Published 2 January 2020

Abstract

We present a Monte Carlo algorithm based on the stochastic approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is stochastic approximation with a dynamic update factor (SAD), which dynamically adjusts the update factor γt during the course of the simulation. We test this method on a square-well fluid and a 31-atom Lennard-Jones cluster and compare the convergence behavior of several related Monte Carlo methods. We find that both the SAD and 1/t-Wang-Landau (1/t-WL) methods rapidly converge to the correct density of states without the need for the user to specify an arbitrary tunable parameter t0 as in the case of SAMC. SAD requires as input the temperature range of interest, in contrast with 1/t-WL, which requires that the user identify the interesting range of energies. The convergence of the 1/t-WL method is very sensitive to the energy range chosen for the low-temperature heat capacity of the Lennard-Jones cluster. Thus, SAD is more powerful in the common case in which the range of energies is not known in advance.

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  • Received 10 May 2019
  • Revised 26 November 2019

DOI:https://doi.org/10.1103/PhysRevE.101.013301

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Jordan K. Pommerenck, Tanner T. Simpson, Michael A. Perlin, and David Roundy

  • Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA

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Issue

Vol. 101, Iss. 1 — January 2020

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