Comparison of analytic and numerical results in the XY-model

TL;DR

This paper compares high-precision Monte Carlo simulations of the 2D XY-model with analytical predictions, confirming the continuum limit matches sine-Gordon theory, emphasizing the importance of logarithmic lattice artifact decay in extrapolation.

Contribution

It provides a detailed numerical verification of the continuum approach for the XY-model, incorporating a predicted logarithmic decay of lattice artifacts for accurate extrapolation.

Findings

Monte Carlo results agree with sine-Gordon predictions

Logarithmic decay of lattice artifacts is essential for accurate continuum extrapolation

High-precision data supports the continuum approach of the XY-model

Abstract

We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with analytic predictions for the finite volume energy spectrum based on the equivalence with sine-Gordon theory. To come to this conclusion it was essential to use an also predicted form of logarithmic decay of lattice artifacts for the extrapolation.