Interplay of topological and structural defects in the 2D XY model

TL;DR

This paper investigates how vortices and impurities interact in the 2D XY model, revealing how impurities lower the BKT transition temperature, supported by theoretical analysis and Monte Carlo data.

Contribution

It provides a theoretical description of impurity effects on the BKT transition, comparing phenomenological and Villain model approaches.

Findings

Impurities reduce the BKT transition temperature.

Theoretical predictions align with Monte Carlo simulations.

Vortex-impurity interactions are characterized from two models.

Abstract

The present work is devoted to the investigation of the interaction between vortices (topological defects) and site-impurities (structural defects) in the 2D XY model and its influence on the well-known properties of the pure system. The main goal is a theoretical description of the Berezinskii-Kosterlitz-Thouless (BKT) temperature reduction by quenched non-magnetic impurities, based on the vacancy-vortex interactions and the vortex-pair dissociation mechanism of the transition. The non-magnetic impurity interaction with a system of vortices can be found either from the phenomenological theory of topological defects or from the Villain model. We take both paths and compare the results obtained. Our prediction for the BKT temperature reduction is confirmed by the available Monte Carlo data.