Correlations in the low-temperature phase of the two-dimensional XY model

TL;DR

This paper uses Monte Carlo simulations and conformal mapping to accurately determine the temperature-dependent correlation exponent in the 2D XY model's critical phase, revealing no logarithmic corrections at the transition.

Contribution

It introduces a method to easily extract the correlation exponent at any temperature using conformal mapping, and provides new evidence on the absence of logarithmic corrections at the Kosterlitz-Thouless transition.

Findings

Accurate numerical determination of eta_sigma(T) up to the transition temperature.

Good agreement with Berezinskii's harmonic approximation at low temperatures.

Evidence suggesting no logarithmic corrections at the transition.

Abstract

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with fixed boundary conditions. Using a conformal mapping it is very easy to deduce the exponent eta_sigma(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of eta_sigma(T) is obtained numerically with a good accuracy up to the Kosterlitz-Thouless transition temperature. At very low temperatures, a good agreement is found with Berezinskii's harmonic approximation. Surprisingly, we show some evidence that there are no logarithmic corrections to the behaviour of the order parameter density profile (with symmetry breaking surface fields) at the Kosterlitz-Thouless transition temperature.