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

TL;DR

This paper compares theoretical epsilon-expansion predictions with Monte Carlo simulations for universal order parameter profiles in critical adsorption and the extraordinary transition, highlighting the importance of correct asymptotic behaviors.

Contribution

It introduces a novel RG scheme with z-dependent amplitude renormalization to accurately extrapolate epsilon-expansion results to three dimensions and compare with Monte Carlo data.

Findings

Good agreement between extrapolated epsilon-expansion and Monte Carlo results.

Correct asymptotic behaviors are crucial for meaningful extrapolations.

The approach aligns with some experimental observations.

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.