Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy

TL;DR

This paper investigates the complex interactions between spin waves and vortices in the 2D XY model, introducing a modified model and a two-step theoretical approach that aligns well with Monte-Carlo simulations, enhancing understanding of vortex unbinding.

Contribution

The study develops optimized initial conditions for BKT flow equations and applies a modified XY model with increased vortex fugacity to better understand vortex-spin wave interplay.

Findings

Two-step approach accurately reproduces Monte-Carlo results

Modified XY model with high vortex fugacity studied

Vortex unbinding described by nonperturbative functional renormalisation group

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes universal vortex unbinding in many two-dimensional systems, including the paradigmatic XY model. However, most of these systems present a complex interplay between excitations at different length scales that complicates theoretical calculations of nonuniversal thermodynamic quantities. These difficulties may be overcome by suitably modifying the initial conditions of the BKT flow equations to account for noncritical fluctuations at small length scales. In this work, we perform a systematic study of the validity and limits of this two-step approach by constructing optimised initial conditions for the BKT flow. We find that the two-step approach can accurately reproduce the results of Monte-Carlo simulations of the traditional XY model. In order to systematically study the interplay between vortices and spin-wave excitations, we introduce a modified XY model with increased vortex fugacity. We present large-scale Monte-Carlo simulations of the spin stiffness and vortex density for this modified XY model and show that even at large vortex fugacity, vortex unbinding is accurately described by the nonperturbative functional renormalisation group.