High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

TL;DR

This paper extends the high-temperature series for the 2D XY model's free energy to order 48, providing strong evidence that the phase transition aligns with the Kosterlitz-Thouless type, using an improved finite lattice method.

Contribution

The authors developed an improved algorithm to extend the high-temperature series of the XY model's free energy to order 48, surpassing previous limits.

Findings

Series behavior matches Kosterlitz-Thouless transition predictions

High-precision data supports the phase transition type

Extended series enhances understanding of 2D XY model

Abstract

We extend the high-temperature series of the free energy for the XY model in two dimensions to order $\beta^{48}$ from the previous order of $\beta^{22}$ by applying the improved algorithm of the finite lattice method. The long series obtained enables us to conclude that the behavior of the free energy is consistent in high accuracy with what is expected when the phase transition of the model is of the Kosterlitz-Thouless type .