The two dimensional XY model at the transition temperature: A high precision Monte Carlo study

TL;DR

This high-precision Monte Carlo study of the 2D XY model at the Kosterlitz-Thouless transition confirms the inverse transition temperature and investigates logarithmic corrections to magnetic susceptibility.

Contribution

The paper provides precise Monte Carlo data for the 2D XY model at criticality, confirming theoretical predictions for finite size scaling and the transition temperature.

Findings

Confirmed inverse transition temperature beta_{KT}=1.1199

Derived finite size scaling behavior of correlation length ratio

Addressed logarithmic corrections of magnetic susceptibility

Abstract

We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature.