Local-functional theory of critical adsorption

Local-functional methods are applied to critical adsorption in three-dimensional Ising-like systems. The universal order-parameter-profile scaling functions, $P_{\pm }\mathrm{}\left(x\right),$ along the critical isochore $\mathrm{}(+)\mathrm{}$ and phase boundary $\left(-\right),$ are calculated along with their associated universal amplitudes. Good agreement is found with the results of Monte Carlo simulations. General properties of $P_{\pm }\mathrm{}\left(x\right)\mathrm{}$ for small and large scaled distance, x, are elucidated. An order-parameter scaling function, $P_c\mathrm{}\left(x\right),$ for critical adsorption along the critical isotherm is introduced and calculated.