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

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 $(ρ)$. As expected, our calculation shows that the BKT temperature decreases as the spin vacancies increase. There is a critical dilution $ρ_c \approx 0.3$ 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.