Non mean-field behaviour of critical wetting transition for short-range forces

TL;DR

This study uses Monte Carlo simulations to investigate the critical wetting transition in three dimensions, revealing deviations from mean-field behavior and estimating effective critical exponents consistent with theoretical predictions.

Contribution

The paper demonstrates that the critical wetting transition in 3D exhibits non-mean-field behavior and refines finite size scaling methods for more accurate analysis.

Findings

Effective critical exponents estimated at ~1.76 and ~1.85.

Deviations from mean-field behavior confirmed.

Finite size scaling approach requires modifications in 3D.

Abstract

Critical wetting transition for short-range forces in three dimensions ($d=3$) is reinvestigated by means of Monte Carlo simulation. Using anisotropic finite size scaling approach, as well as approaches that do not rely on finite size scaling, we show that the critical wetting transition shows clear deviation from mean-field behaviour. We estimate that the effective critical exponent $\nu_{\|}^{\textrm{eff}}=1.76\pm 0.08$ for $J/kT=0.35$ and $\nu_{\|}^{\textrm{eff}}=1.85\pm 0.07$ for $J/kT=0.25$. These values are in accord with predictions of Parry {\it et al.} [Phys. Rev. Lett. {\bf 100}, 136105 (2008)]. We also point out that the anisotropic finite size scaling approach in $d=3$ requires additional modification in order to reach full consistency of simulational results.