Superfluid transition and specific heat of the 2D x-y model: Monte Carlo simulation

TL;DR

This paper uses large-scale Monte Carlo simulations to accurately analyze the superfluid transition and specific heat of the 2D x-y model, providing insights relevant to experiments on thin helium films.

Contribution

It offers high-precision Monte Carlo results for the superfluid transition temperature and specific heat, confirming previous estimates and analyzing size independence of specific heat features.

Findings

Superfluid transition temperature consistent with prior studies.

Specific heat peak shape and position are size-independent for large lattices.

Results have implications for interpreting experiments on He-4 thin films.

Abstract

We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of linear size L up to 4096. Our estimate for the superfluid transition temperature is consistent with those furnished in all previous studies. The specific heat displays a well-defined peak, whose shape and position are independent of the size of the lattice for L > 256, within the statistical uncertainties of our calculations. The implications of these results on the interpretation of experiments on adsorbed thin films of He-4 are discussed.