Scaling of the superfluid density in superfluid films

TL;DR

This paper investigates how the superfluid density in films scales with thickness by simulating the $x-y$ model, revealing a universal scaling behavior that aligns with experimental data and conventional theories.

Contribution

It introduces a universal scaling relation for superfluid density in films using an effective thickness, bridging simulation results with experimental observations.

Findings

Scaling relations reduce to conventional forms for large thickness

Universal curve achieved with effective thickness

Simulation results match experimental data using the same critical exponent

Abstract

We study scaling of the superfluid density with respect to the film thickness by simulating the $x-y$ model on films of size $L \times L \times H$ ($L >> H$) 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 value of $\nu = 0.6705$.