Numerical confirmation of analytic predictions for the finite volume mass gap of the XY-model

TL;DR

This paper numerically confirms the analytic predictions for the finite volume mass gap of the 2D XY-model, validating the sine-Gordon theory correspondence and the predicted lattice artifact decay.

Contribution

It provides high-precision numerical simulations that verify the analytic predictions for the XY-model's mass gap and finite size behavior in the continuum limit.

Findings

Numerical results agree with analytic predictions in the continuum limit.

Logarithmic decay of lattice artifacts was crucial for accurate extrapolation.

High-precision simulation confirms the sine-Gordon theory correspondence.

Abstract

Recent exact predictions for the massive scaling limit of the two dimensional XY-model are based on the equivalence with the sine-Gordon theory and include detailed results on the finite size behavior. The so-called step-scaling function of the mass gap is simulated with very high precision and found consistent with analytic results in the continuum limit. To come to this conclusion, an also predicted form of a logarithmic decay of lattice artifacts was essential to use for the extrapolation.