CRITICAL CASIMIR FORCE SCALING FUNCTIONS OF THE MEAN SPHERICAL MODEL IN 2 < d ≤ 3 DIMENSIONS FOR NONPERIODIC BOUNDARY CONDITIONS

Finite-size effects are investigated in the mean spherical model in film geometry with nonperiodic boundary conditions above and below bulk T_c. We have obtained exact results for the excess free energy and the Casimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixed boundary conditions in 2 < d ≤ 3 dimensions. Analytic results are presented in 2 < d < 3 dimensions for Dirichlet boundary conditions and for d = 3 for Neumann-Dirichlet boundary conditions. We find an unexpected leading size dependence ∝ C_± t/L² of the Casimir force, with dfferent amplitudes C₊ and C_- above and below T_c for large L at fixed t ≡ (T - T_c)/T_c ≠ 0 for other than periodic boundary conditions.