Order-Parameter Profile in Semi-Infinite Systems at Criticality

Abstract

A description of the decay into the bulk of surface perturbations in a system at its critical point is presented. The description, justified by detailed renormalization-group calculations, yields asymptotic order-parameter decay, $z^{-\frac{(d-2+\eta )}{2}}$, along with power-law behavior connected with surface exponents under suitable conditions. Comparison with the phenomenological theories of Widom and of Fisher and de Gennes is also made.