Improving Wang-Landau sampling with adaptive windows

TL;DR

This paper introduces adaptive windowing in Wang-Landau sampling to eliminate boundary effects, enabling more reliable simulations of larger systems in statistical physics.

Contribution

The authors develop an adaptive window approach for Wang-Landau sampling that dynamically adjusts window boundaries during simulation.

Findings

Eliminates boundary effects in density of states estimation.

Extends the range of system sizes reliably studied with WLS.

Improves accuracy of thermodynamic functions in lattice models.

Abstract

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) are shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.