Fast Algorithm to Calculate Density of States

TL;DR

This paper introduces a fast, asymptotically accurate algorithm for calculating the density of states using a modified Wang-Landau method, which avoids error saturation and exhibits universal interface growth behavior.

Contribution

The paper presents a novel algorithm that improves the convergence speed and accuracy of density of states calculations by employing a 1/t modification in the Wang-Landau method.

Findings

Density of states converges as 1/sqrt(t) avoiding saturation.

The energy histogram interface growth belongs to the random deposition universality class.

The method achieves asymptotic accuracy in density of states estimation.

Abstract

An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by a function of time, F(t)=1/t, for large time. As a consequence, the calculated density of state, gm(E,t), approaches asymptotically the exact value gex(E) as 1/sqrt(t), avoiding the saturation of the error. It is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class.