CRITICAL-BEHAVIOR AT THE EXTRAORDINARY TRANSITION - 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 h1; Renormalization-group improved perturbation theory is applied to the standard semi-infinite scalar phi4 model in d = 4 - epsilon dimensions to compute the order-parameter profile to one-loop order both for temperatures T with tau = (T - T(cb))/T(cb) greater than or similar to 0 and tau less than or similar to 0. The associated scaling functions are found to cross smoothly over from their short-distance behavior for distances Z << xi(b) (= bulk correlation length) to their long-distance behavior for z >> xi(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 Absolute value ot tau2-alpha singularity of the surface magnetization m1 plus a regular background term; that is, in contrast to results published recently by other authors, the amplitudes A+ and A- of the contributions A+/-tau to m1 linear in tau > 0 or 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 = +infinity and h1 = infinity) agree with the previous ones pertaining to the extraordinary-transition fixed point at c = -infinity and h1 = 0.