Critical Phenomena in Systems of Finite Thickness. III. Specific Heat of an Ideal Boson Film

The specific heat at constant density of an ideal-Bose-fluid film of thickness $L=l{\rho }^{-\frac{1}{3}}$, but infinite lateral extent, is calculated analytically to order $l^{-2\mathrm{}}$. Both hard-wall and periodic boundary conditions are considered. Good agreement with the numerical calculations of Goble and Trainor for the total specific heat under hard-wall conditions is obtained down to $l\simeq 10$. In the critical region, the large-$l$ behavior accords with the scaling theory of finite-size effects. The appropriate scaling functions and the surface specific heat are explicitly calculated.