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. 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≃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.