Absence of hyperuniversality in critical films

Scaling density profiles O(N) symmetric systems confined between two parallel plates with a large separation L are analyzed by field-theoretical methods for a continuous phase transition at bulk criticality ${\mathit{T}}_{\mathit{c},}$b in spatial dimension d=4-ɛ. At distances z≪L from one wall a the profile contains a perturbation ${\mathit{B}}_{\mathit{a},}$b(z/L${)}^{\mathit{d}}$ induced by the distant wall b. In contrast to previous expectations the ratio of the universal amplitude ${\mathit{B}}_{\mathit{a},}$b and the corresponding Casimir amplitude is not hyperuniversal, i.e., not independent of both surface universality classes characterizing the walls a and b.