Specific heat of bosons among periodical layers

It is well known that the specific heat of a 3D ideal boson gas shows continuity as a function of the temperature. However, interactionless bosons among periodic plane layers with variable penetrability, show a specific heat jump at the critical temperature, which increases as a function of the layer impenetrability. The jump resembles that of a conventional superconductor instead of that of a laminar cuprate. We expect that inclusion of inter-boson interaction leads to a more realistic specific heat.