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

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 ${\mathit{h}}_{1}$. Renormalization-group improved perturbation theory is applied to the standard semi-infinite scalar ${\mathrm{\ensuremath{\varphi}}}^{4}$ model in d=4-\ensuremath{\epsilon} dimensions to compute the order-parameter profile to one-loop order both for temperatures T with \ensuremath{\tau}\ensuremath{\equiv}(T-${\mathit{T}}_{\mathit{c}\mathit{b}}$)/${\mathit{T}}_{\mathit{c}\mathit{b}}$\ensuremath{\gtrsim}0 and \ensuremath{\tau}\ensuremath{\lesssim}0. The associated scaling functions are found to cross smoothly over from their short-distance behavior for distances z\ensuremath{\ll}${\ensuremath{\xi}}_{\mathit{b}}$ (=bulk correlation length) to their long-distance behavior for z\ensuremath{\gg}${\ensuremath{\xi}}_{\mathit{b}}$ 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 \ensuremath{\Vert}\ensuremath{\tau}${\mathrm{\ensuremath{\Vert}}}^{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ 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 ${\mathit{A}}_{\mathrm{\ensuremath{-}}}$ of the contributions ${\mathit{A}}_{\ifmmode\pm\else\textpm\fi{}}$\ensuremath{\tau} to ${\mathit{m}}_{1}$ linear in \ensuremath{\tau}>0 or \ensuremath{\tau}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=+\ensuremath{\infty} and ${\mathit{h}}_{1}$=\ensuremath{\infty}) agree with the previous ones pertaining to the negative-c-transition fixed point at c=-\ensuremath{\infty} and ${\mathit{h}}_{1}$=0.