Abstract
The surface critical behavior of semi-infinite systems belonging to the Ising universality class with short-range interactions is investigated for supercritical surface enhancement -c>0 and vanishing surface field . Renormalization-group improved perturbation theory is applied to the standard semi-infinite scalar model in d=4-ε dimensions to compute the order-parameter profile to one-loop order both for temperatures T with τ≡(T-)/≳0 and τ≲0. The associated scaling functions are found to cross smoothly over from their short-distance behavior for distances z≪ (=bulk correlation length) to their long-distance behavior for z≫ without showing the peculiar nonmonotonic behavior asserted by Peliti and Leibler [J. Phys. C 16, 2635 (1983)]. Furthermore, the short-distance behavior of the profiles is shown to be fully consistent with a ‖τ singularity of the surface magnetization plus a regular background term; that is, in contrast to results published recently by other authors, the amplitudes and of the contributions τ to linear in τ>0 or τ<0 agree to one-loop order. Finally, we confirm that the universal profiles for the critical adsorption of fluids (governed by the critical-adsorption fixed point at c=+∞ and =∞) agree with the previous ones pertaining to the negative-c-transition fixed point at c=-∞ and =0.
- Received 16 September 1992
DOI:https://doi.org/10.1103/PhysRevB.47.5841
©1993 American Physical Society