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