Monte Carlo study of the critical temperature for the planar rotator model with nonmagnetic impurities

TL;DR

This study uses Monte Carlo simulations to analyze how nonmagnetic impurities affect the Berezinskii-Kosterlitz-Thouless transition temperature in a two-dimensional planar rotator model, revealing a critical impurity concentration where the transition vanishes.

Contribution

It provides the first detailed Monte Carlo analysis of impurity effects on the BKT transition in the 2D planar rotator model, including an analytical study of vortex-impurity interactions.

Findings

BKT temperature decreases with increasing impurity concentration.

Critical impurity concentration $ ho_c \\approx 0.3$ where $T_{BKT}$ becomes zero.

Analytical model supports simulation results.

Abstract

We performed Monte Carlo simulations to calculate the Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{BKT}$ for the two-dimensional planar rotator model in the presence of nonmagnetic impurity concentration $(\rho)$. As expected, our calculation shows that the BKT temperature decreases as the spin vacancies increase. There is a critical dilution $\rho_c \approx 0.3$ at which $T_{BKT} =0$. The effective interaction between a vortex-antivortex pair and a static nonmagnetic impurity is studied analytically. A simple phenomenological argument based on the pair-impurity interaction is proposed to justify the simulations.