Monte Carlo study of the XY-model on Sierpnski carpet

摘要

We have performed a Monte Carlo study of the classical XY-model on a Sierpi\'nski carpet, which is a planar fractal structure with infinite order oframification and fractal dimension 1.8928. We employed the Wolff clusteralgorithm in our simulations and our results, in particular those for thesusceptibility and the helicity modulus, indicate the absence offinite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transition in thissystem.