Critical Phenomena in Systems of Finite Thickness. II. Ideal Bose Gas

Abstract

The grand potential pressure of an ideal boson film which is infinite in d-1 dimensions (d > 2) but of finite thickness L in the dth dimension is analysed in the limit L -+ CX), to order L -d. Across the film (i) periodic, (ii) antiperiodic, and (iii) hard wall boundary conditions are applied. The corresponding shifts in the critical temperature Te.iL) are found to vary, for large L, as (i) L -d+2 for all d ;;:. 3, (ii) L-1, L -2lnL, and L -2 for d = 3,4, and ;;:. 5 respectively, and (iii) L -1lnL and L -1 for d = 3 and ;;:. 4. With hard wall boundary conditions, the critical temperature of a sufficiently thick film exceeds that of the bulk, while the other boundary conditions depress Te. The bulk critical region is asymptotically "rounded" on a scale set by the bulk correlation length matching the thickness L in accord with the scaling theory of finite-size effects.