Heat-capacity scaling function for confined superfluids

Abstract

We study the specific-heat scaling function of confined superfluids using Monte Carlo simulation. While the scaling function is insensitive to the microscopic details, it depends on the confining geometry and boundary conditions (BC's). In the present work we have studied (a) cubic geometry with open BC's in all three directions and (b) parallel-plate (film) geometry using open BC's along the finite dimension and periodic BC's along the other two dimensions. We find that the specific-heat scaling function is significantly different for the two different geometries studied. The scaling function for each geometry (a) or (b) is very different when compared to that obtained for the same geometry but with periodic BC's. On the contrary, we find that in case (b) the calculated scaling function is very close to the earlier calculated using Dirichlet instead of open BC's. This demonstrates that Dirichlet and open boundary conditions act in a similar way. Our results for both scaling functions obtained for the parallel-plate geometry and for cubic geometry with open BC's along the finite dimensions are in very good agreement with recent very-high-quality experimental measurements with no free parameters.