Thermodynamic properties of ideal particles in a finite number of layers

For ideal particles in a finite multilayer system with free boundary conditions and a hopping amplitude, t, between neighbouring layers, we calculate the temperature dependence of the specific heat and the magnetic susceptibility. In spite of the fact that the excitation gap in the discrete direction is wiped out by the continuous 2-D spectrum, Schottky anomaly persists for both classical and quantum particles. Although finite-temperature Bose condensation only occurs when the layer number, n, is strictly infinite, we find the tendency towards condensation to happen much earlier and to be responsible for a second peak in the specific heat of bosons when n is large. The temperature dependence of the susceptibility for bosons also exhibits a similar dimensional transition as n increases, but the critical n is different from that for the specific heat.