Universal order-parameter profiles for critical adsorption and the extraordinary transition: a comparison of epsilon-expansion and Monte Carlo results

Smock, M.; Diehl, H. W.; Landau, D. P.

Universal order-parameter profiles for critical adsorption and the extraordinary transition: a comparison of epsilon-expansion and Monte Carlo results

Authors

Smock, M.

Diehl, H. W.

Landau, D. P.

Description

The universal, scaled order parameter profiles $P_{\pm}(z/ξ)$ 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 $P_{\pm}(ζ)\simζ^{-β/ν}$ at 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.
14 Pages (RevTex V3.0), including two figures formatted as .eps files