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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.
Type
Preprint
Publication Date
Feb 17, 1994
Submission Date
Feb 17, 1994
Identifiers
arXiv ID: cond-mat/9402068
Source
arXiv
License
Unknown
External links

Abstract

The universal, scaled order parameter profiles $P_{\pm}(z/\xi)$ 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, $\xi (T)$ is the bulk correlation length, and the subscript $+$ ($-$) refers to the approach from above (below) $T_c$. Recent results to first order in the $\epsilon=4-d$ 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 $\zeta$ as well as the known algebraic behavior $P_{\pm}(\zeta)\sim\zeta^{-\beta/\nu}$ at small $\zeta$ 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.

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