Critical Wall Perturbations: Scaling and Renormalization Group

The influence at criticality of a "far" wall on the order parameter close to a "near" wall as discussed by Fisher and de Gennes is recast in a form more suitable for microscopic analysis. An argument beyond ordinary scaling is presented which yields the perturbation exponent d*=d for longitudinal perturbations and d_⊥*=d-1 for transverse perturbations. These results are consistent with explicit renormalization-group computations to O(ε=4-d) which involve solution of the nonlocal equation of state.