Wang-Landau algorithm for continuous models and joint density of states

TL;DR

This paper introduces a modified Wang-Landau algorithm tailored for continuous models, enabling efficient calculation of the joint density of states in large-scale ferromagnetic systems, providing richer insights than single-variable densities.

Contribution

The paper develops a modified Wang-Landau algorithm for continuous models and demonstrates its efficiency in calculating joint densities of states in large ferromagnetic systems.

Findings

Successfully computed joint density of states for large Heisenberg models

Enhanced efficiency in continuous models with thousands of degrees of freedom

Provides more detailed information than single-variable density of states

Abstract

We present modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density of states contains more information than the density of states of a single variable--energy, but is also much more time-consuming to calculate. We discuss the strategies to perform this calculation efficiently for models with several thousand degrees of freedom, much larger than other continuous models studied previously with the Wang-Landau algorithm.