Critical Casimir forces in the presence of random surface fields

TL;DR

This study investigates how random surface fields affect critical Casimir forces in thin Ising-like films, revealing that weak disorder is irrelevant but can significantly enhance forces in thin films with strong disorder.

Contribution

It provides a finite-size scaling analysis and Monte Carlo simulations showing the impact of random surface fields on critical Casimir forces in the ordinary transition universality class.

Findings

Weak disorder does not alter the scaling behavior of CCF.

Random surface fields can significantly increase CCF strength in thin films.

The presence of RSF shifts the extremum of the CCF scaling function towards lower temperatures.

Abstract

We study critical Casimir forces (CCF) $f_{\mathrm C}$ for films of thickness $L$ which in the three-dimensional bulk belong to the Ising universality class and which are exposed to random surface fields (RSF) on both surfaces. We consider the case that, in the absence of RSF, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We carry out a finite-size scaling analysis and show that for weak disorder CCF still exhibit scaling, acquiring a random field scaling variable $w$ which is zero for pure systems. We confirm these analytic predictions by MC simulations. Moreover, our MC data show that $f_{\mathrm C}$ varies as $f_{\mathrm C}(w\to 0)-f_{\mathrm C}(w=0)\sim w^2$. Asymptotically, for large $L$, $w$ scales as $w \sim L^{-0.26} \to 0$ indicating that this type of disorder is an irrelevant perturbation of the ordinary surface universality class. However, for thin films such that $w \simeq 1$, we find that the presence of RSF with vanishing mean value increases significantly the strength of CCF, as compared to systems without them, and shifts the extremum of the scaling function of $f_{\mathrm C}$ towards lower temperatures. But $f_{\mathrm C}$ remains attractive.