CRITICAL-BEHAVIOR NEAR A SYMMETRY-BREAKING SURFACE AND THE STRESS TENSOR

The critical behavior near a surface that breaks the order parameter s ymmetry is analyzed with field-theoretic renormalization-group methods . We study the short-distance expansions of the order parameter and th e energy density about the surface and investigate various density pro files and correlation functions in the half-space and film geometries. Our results confirm Cardy's conjecture that the stress-energy tensor appears as the leading surface density. Its universal prefactor C in t he expansions determines several physical properties of interest in th e critical adsorption of fluids: In a film at the bulk critical temper ature T(c), C determines the amplitude ratio of the Fisher-de Gennes d istant-wall correction to the order-parameter profile and the Casimir correction to the free energy. In the half-space close to T(c), C dete rmines the amplitude ratio of the (z/xi)d term in the order parameter profile to the Ferer-Stauffer-Wortis term in the bulk free energy. Her e z is the distance from the surface and xi the bulk correlation lengt h. In the half-space at T(c), C also determines the universal short-di stance amplitudes of layer susceptibilities, which should be observabl e in computer experiments. We calculate C to second order in epsilon = 4 - d and estimate its value for d = 3. C is closely related to the s tress-stress correlation in a half-space, for which we obtain the bulk to surface crossover. We present a simple argument showing why this c rossover depends, in general, on the surface universality class except in two dimensions.