Berezinskii-Kosterlitz Thouless Phase Transition in Superconducting Two Dimensional Triangular Lattice

Berezinskii-Kosterlitz Thouless (BKT) transition is a phase transition on spin vectors at 2 dimensional lattice from bound vortex anti vortex at low temperatures to unpaired vortices and anti-vortices above critical temperature. Those two phases di er in the way their long distance correlations decay, as a power law (at low temperatures) or exponentially above critical temperature. In disordered systems these correlations propagate through favorable paths, corresponding to where the short range interactions are stronger.Thus in such systems, the BKT transition may be viewed as a loss of the percolating correlation network. The study of this transition and the point in which global coherence is lost has high implications on our understanding of mesoscopic systems modeled by XY spin model, in particular, superconductivity in thin lms. In the article produced by Amir Erez and Yigal Meir [5]the behavior of such a two dimensional spin system on a square lattice has been studied using Monte Carlo method. In these simulations, where the nearest neighbor spin couplings were taken from an exponentially wide distribution, the critical temperature was found to be almost independent of disorder the width of the distribution as along as the median of the distribution remained constant. This was taken as a con rmation of thee percolation scenario, as the bond percolation threshold for the square lattice is exactly 1/2. In my project I intend to build similar simulations to study the behavior of such systems on a triangular lattice, and study the relation between the critical temperature and the parameters of the distribution. Since the percolation threshold for the triangular lattice is di erent from 1/2, this will allow us to determine whether indeed it is the percolation threshold that determines the BKT transition in disordered lms.