Heat capacity scaling function for confined superfluids

We study the specific heat scaling function of superfluids confined in cubic geometry and in parallel-plate (film) geometry with open boundary conditions (BC) along the finite dimensions using Monte Carlo simulation. For the case of cubic geometry for the superfluid order parameter we apply open BC in all three directions. We also calculated the specific heat scaling function for the parallel-plate confinement using open BC along the finite dimension and periodic BC along the other two dimensions and we find it to be very close to the earlier calculated using Dirichlet instead of open BC. We find that the specific heat scaling function is significantly different for the two different geometries studied. In addition, we generally find that the scaling function for a fixed given geometry when calculated with open BC is quite close to that calculated with Dirichlet BC, while when calculated with periodic BC is quite different. Our results for both the scaling functions obtained for the parallel-plate geometry and for cubic geometry with open BC along the finite dimensions are in very good agreement with the recent very high quality experimental measurements with no free parameters.