Free energy and specific heat of critical films and surfaces

Based on the field-theoretical renormalization-group theory for O(N) symmetric systems in 4-e dimensions, the free energy of critical films confined between two parallel plates at distance L is analyzed. For five different boundary conditions and for temperatures above and at the bulk critical temperature T c,b , the analytic expressions of the universal scaling functions are derived and discussed. At bulk criticality, the scaling functions reduce to universal amplitudes commonly known as Casimir amplitudes