Influence of quenched dilution on the quasi-long-range ordered phase of the 2d XY model

TL;DR

This paper investigates how non-magnetic impurities affect the quasi-long-range order in the 2D XY model, confirming the BKT transition remains valid and analyzing the critical exponent behavior through Monte Carlo simulations.

Contribution

It provides new Monte Carlo estimates of the critical exponent at various dilutions and supports findings with spin-wave calculations.

Findings

Universality class remains unchanged with dilution.

Critical exponent η varies with dilution.

Spin-wave calculations support Monte Carlo results.

Abstract

The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent $\eta$ at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations.