The specific heat of superfluids near the transition temperature

TL;DR

This study investigates the specific heat behavior of the $x-y$ model near the transition temperature using Monte Carlo simulations on different lattice geometries, revealing universal scaling functions that differ between film and cubic geometries.

Contribution

It provides the first detailed comparison of finite-size scaling functions for the $x-y$ model in different geometries, highlighting geometry-dependent universal behavior.

Findings

Universal scaling functions are confirmed for both geometries.

Scaling functions differ between film and cubic geometries.

Results agree with experimental and renormalization group data.

Abstract

The specific heat of the $x-y$ model is studied on cubic lattices of sizes $L \times L \times L$ and 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. Periodic boundary conditions were applied in all directions. In the cubic case we obtained the ratio of the critical exponents $\alpha/\nu$ from the size dependence of the energy density at the critical temperature $T_{\lambda}$. Using finite--size scaling theory, we find that while for both geometries our results scale to universal functions, these functions differ for the different geometries. We compare our findings to experimental results and results of renormalization group calculations.