Kosterlitz-Thouless Transition: The Diluted XY model

The effect of nonmagnetic disorder on Berezinskii-Kosterlitz-Thouless (BKT) transition in the two-dimensional ferromagnetic XY model on a square lattice, diluted by randomly placed vacancies can be an important source of information on the role played by vortexes in this transition. The transition temperature T_BKT is determined as a function of vacancy density ρ_v by stiffness ρ and for different size of the lattice. The anomalous behavior for T_BKT when ρ_v is close to the square lattice percolation limit is a consequence of the effect of finite size of lattice and not due the quantum fluctuations as concluded in literature. We obtain that T_BKT falls to zero at ρ_v ≈ 0.40 close to the value 0.41 obtained for the classic model