A New History-Driven Algorithm to Calculate the Density of States

TL;DR

This paper introduces a novel Monte Carlo algorithm that efficiently calculates the density of states for classical models, ensuring detailed balance and convergence to exact values, with potential for high-accuracy extensions.

Contribution

A new history-driven Monte Carlo algorithm for density of states calculation that maintains detailed balance and converges to the exact solution, comparable to existing methods.

Findings

Achieves efficiency similar to Wang-Landau method

Ensures detailed balance in the limit

Can be extended to multicanonical method

Abstract

We present a new Monte Carlo algorithm applying a history-driven mechanism for the calculation of the density of states for classical statistical models. The new method is as efficient as the Wang-Landau method in sampling through the energy range. With the new method, detailed balance is also naturally satisfied in limit and the estimated density of state converges to the exact value. The new method could be easily evolved into the multicanonical method to achieve high accuracy.