Critical behavior at supercritical surface enhancement: Temperature singularity of surface magnetization and order-parameter profile to one-loop order

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 ${\mathit{h}}_1$. Renormalization-group improved perturbation theory is applied to the standard semi-infinite scalar ${\mathrm{\phi }}^4$ model in d=4-ε dimensions to compute the order-parameter profile to one-loop order both for temperatures T with τ≡(T-${\mathit{T}}_{\mathit{c}\mathit{b}}$)/${\mathit{T}}_{\mathit{c}\mathit{b}}$≳0 and τ≲0. The associated scaling functions are found to cross smoothly over from their short-distance behavior for distances z≪${\xi }_{\mathit{b}}$ (=bulk correlation length) to their long-distance behavior for z≫${\xi }_{\mathit{b}}$ 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${\mathrm{\Vert }}^{2\mathrm{-}\mathrm{\alpha }}$ singularity of the surface magnetization ${\mathit{m}}_1$ plus a regular background term; that is, in contrast to results published recently by other authors, the amplitudes ${\mathit{A}}_{+}$ and ${\mathit{A}}_{\mathrm{-}}$ of the contributions ${\mathit{A}}_{\pm }$τ to ${\mathit{m}}_1$ 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 ${\mathit{h}}_1$=∞) agree with the previous ones pertaining to the negative-c-transition fixed point at c=-∞ and ${\mathit{h}}_1$=0.