Monte Carlo study of the critical temperature for the planar rotator   model with nonmagnetic impurities
  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. 
S.A. Leonel, Pablo Zimmermann Coura, A.R. Pereira, L.A.S. M\'ol and   B.V. Costa