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 ${d_{\perp }}^{*}=d-1\mathrm{}$ for transverse perturbations. These results are consistent with explicit renormalization-group computations to $O(\epsilon =4-d)$ which involve solution of the nonlocal equation of state.