Extinction of the Berezinskii-Kosterlitz-Thouless phase transition by nonmagnetic disorder in planar symmetry spin models

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional planar rotator and $XY$ models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster, and over-relaxation techniques. The transition temperature Tc is determined as a function of vacancy density ρvac by finite-size scaling of the helicity modulus and the in-plane magnetic susceptibility. The results for Tc are consistent with those from the much less precise fourth-order cumulant of Binder. Tc is found to decrease monotonically with increasing ρvac, and falls to zero close to the square lattice percolation limit, ρvac≈0.41. The result is physically reasonable: the quasi-long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.