Scaling of the superfluid density in superfluid films

We study scaling of the superfluid density with respect to the film thickness by simulating the x - y model on films of size L x L x H (L much greater than H) using the cluster Monte Carlo. While periodic boundary conditions where used in the planar (L) directions, Dirichlet boundary conditions where used along the film thickness, We find that our results can, be scaled on a universal curve by introducing an effective thickness, In the limit of large H our scaling relations reduce to the conventional scaling forms, Using the same idea we find scaling in the experimental results using the same valve of v = 0.6705.