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arXiv:cond-mat/9503116 · Physical Review Letters

Scaling of the Specific Heat in Superfluid Films

Norbert Schultka, Efstratios Manousakis

Published Oct 2, 1995• 35 citations
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Abstract

We study the specific heat of the $x$- $y$ model on lattices $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}H$ with $L\ensuremath{\gg}H$ (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.

DOI
10.1103/physrevlett.75.2710

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Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices L\ifmmode\times\else\texttimes\fi{}L up to 400\ifmmode\times\else\texttimes\fi{}400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.
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