Scaling of the specific heat in superfluid films

TL;DR

This paper investigates the specific heat behavior of the $x-y$ model in film geometries using Monte Carlo simulations, revealing universal scaling functions that match experimental data without free parameters.

Contribution

It demonstrates that the specific heat in superfluid film models exhibits universal scaling, aligning simulation results with experimental findings.

Findings

Universal scaling function for specific heat obtained

Simulation results agree with experimental data

Scaling collapse observed across different film thicknesses

Abstract

We study the specific heat of the $x-y$ model on lattices $L \times L \times H$ with $L \gg H$ (i.e. on lattices representing a film geometry) using the Cluster Monte--Carlo method. In the $H$--direction we apply Dirichlet boundary conditions so that the order parameter in the top and bottom layers is zero. We find that our results for the specific heat of various thickness size $H$ collapse on the same universal scaling function. The extracted scaling function of the specific heat is in good agreement with the experimentally determined universal scaling function using no free parameters.