Extending the Broad Histogram Method for Continuous Systems

TL;DR

This paper extends the Broad Histogram Monte Carlo method to continuous systems, demonstrating its effectiveness on the 3D XY-model with results comparable to established methods across a broad temperature range.

Contribution

The authors develop a generalized approach for applying the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, broadening its applicability.

Findings

Results agree with Metropolis and Histogram Monte Carlo methods

Efficiently covers a wide temperature range with minimal additional computational effort

Applicable to various systems with continuous degrees of freedom

Abstract

We propose a way of extending the Broad Histogram Monte Carlo method (BHMC) to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model. Our method gives results in excellent agreement with Metropolis and Histogram Monte Carlo simulations and calculates for the whole temperature range 1.2<T<4.7 using only 2 times more computer effort than the Histogram method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.