The Accuracy and Performance Analysis of the 1/t Wang-Landau Algorithm in the Joint Density of States Estimation

TL;DR

This paper evaluates the 1/t Wang-Landau algorithm's accuracy and efficiency in estimating the density of states for a 2D Ising model, highlighting systematic errors, error maxima, and challenges in predicting execution time.

Contribution

It provides a detailed analysis of the 1/t Wang-Landau algorithm's errors, execution time estimation issues, and benefits of simultaneous density of states calculations for improved accuracy.

Findings

Systematic errors decrease with larger lattice sizes.

Error maxima occur near ground state energy and critical point.

Simultaneous calculations improve statistical moment estimates.

Abstract

The 1/t Wang-Landau algorithm is analyzed from the viewpoint of execution time and accuracy when it is used in computations of the density of states of a two-dimensional Ising model. We find that the simulation results have a systematic error, the magnitude of which decreases with increasing the lattice size. The relative error has two maxima: the first one is located near the energy of the ground state, and the second maximum corresponds to the value of the internal energy at the critical point. We demonstrate that it is impossible to estimate the execution time of the 1/t Wang-Landau algorithm in advance when simulating large lattices. The reason is that the criterion for switching to the 1/t mode was not met when the final value of the modification factor was reached. The simultaneous calculations of the density of states for energy and magnetization are shown to lead to higher accuracy in estimating statistical moments of internal energy.