Density of states of a two dimensional XY model from Wang-Landau algorithm

TL;DR

This paper accurately calculates the density of states for a 2D XY model using a combined Wang-Landau and analytical approach, revealing phase transition features and proposing a general method for continuous models.

Contribution

It introduces a novel combined simulation and analytical method to compute the density of states for continuous models like the 2D XY model.

Findings

Accurate density of states for 16x16, 24x24, 32x32 lattices.

Thermodynamic quantities derived from density of states.

Signs of phase transition observed in entropy curve.

Abstract

Using Wang-landau algorithm combined with analytic method, the density of states of two dimensional XY model on square lattices of sizes $16\times16$, $24\times24$ and $32\times32$ is accurately calculated. Thermodynamic quantities, such as internal energy, free energy, entropy and specific heat are obtained from the resulted density of states by numerical integration. From the entropy curve symptoms of phase transition is observed. A general method of calculation of the density of states of continuous models by simulation combined with analytical method is proposed.