The density of states of classical spin systems with continuous degrees of freedom

TL;DR

This paper extends a density of states computation method to classical spin systems with continuous degrees of freedom, enabling microcanonical analysis of phase transitions in models like the 3D XY model.

Contribution

It introduces an extension of a density of states algorithm from discrete to continuous systems, facilitating direct analysis of critical phenomena.

Findings

Successfully computed the density of states for the 3D XY model.

Demonstrated that critical quantities can be derived from the density of states.

Validated the method's effectiveness for continuous degrees of freedom.

Abstract

In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the entropy $S = \ln \Omega$ where $\Omega$ is the density of states. Obviously, the density of states has to be known with very high accuracy for this kind of analysis. Important progress has been achieved recently in the computation of the density of states of classical systems, as new types of algorithms have been developed. Here we extend one of these methods, originally formulated for systems with discrete degrees of freedom, to systems with continuous degrees of freedoms. As an application we compute the density of states of the three-dimensional XY model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values.