Broad Histogram Method for Continuous Systems: the XY-Model

TL;DR

This paper introduces a generalized Broad Histogram Monte Carlo method for continuous systems, demonstrating its efficiency and accuracy on the 3D XY-model across a broad temperature range, outperforming traditional methods in computational time.

Contribution

The authors develop a novel implementation of the Broad Histogram Monte Carlo method tailored for continuous systems and validate it on the 3D XY-model, showing improved efficiency over standard approaches.

Findings

Excellent agreement with Metropolis results for key thermodynamic quantities.

Faster computation than Metropolis for multiple temperature points.

Efficiently covers a wide temperature range with minimal additional effort.

Abstract

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo 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.