Universal order‐parameter profiles for critical adsorption and the extraordinary transition: A comparison of ϵ expansion and Monte Carlo results

Abstract

Abstract The universal, scaled order parameter profiles P ± ( z /ξ) for critical adsorption of a fluid or fluid mixture onto a wall or interface, and for the extraordinary transition of the semi‐infinite Ising model, are discussed theoretically, where z is the distance from the interface, ξ( T ) is the bulk correlation length, and the subscript + (‐) refers to the approach from above (below) T c . Recent results to first order in the ϵ = 4– d expansion are extrapolated to d = 3 space dimensions and compared with new Monte Carlo results. In order to obtain meaningful extrapolations it is crucial that both the exponential decay at large ζ as well as the known algebraic behavior P ±(ζ)∼ζ −β/ v small ζ be correctly reproduced. To this end a recently developed novel RG scheme involving a z dependent amplitude renormalization is used. Reasonable agreement of our extrapolations with the Monte Carlo results and some experimental results is obtained.