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

Abstract

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 vac 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 vac, and falls to zero close to the square lattice percolation limit, vac 0.41. The result is physically reasonable: the quasi-longrange orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.