The BKT phase transition in the diluted XY Model

The Berezinskii - Kosterliz - Thouless phase transition (BKT) in the diluted XY Model is studied in detail with Monte Carlo simulations using the Wang-Landau algorithm. The transition temperature, $T_{BKT}$, was found by the finite size scaling of the helicity modulus and the in-plane magnetic susceptibility, for various magnetics sites density. The spin-spin correlation function was calculated, for all spins, and for those who are within the cluster that percolates, in temperatures after and below the $T_{BKT}$, for various sizes lattices. We intend, using these results, discuss the mechanism of the unbinding of the vortices - antivortices pairs in the transition process. The position of this pairs and the vortices and antivortices density was calculated for various magnetics sites density. A well accepted theory suggests that this is the main mechanism responsible for the transition. However, we observed that vortices do not move for long distances through the lattice and in the vacancies neighborhood it can be pinned there for a long period of time, then if the transition occurs even with pinned vortices, these can not be responsible for the transition, and another mechanism should be observed. There is another theory which suggests such polymerizations walls domain is responsible for transition. We would like to thank the partial support of this project given by FAPEMIG and CNPq.