Critical Casimir torques and forces acting on needles in two spatial dimensions

TL;DR

This study explores the universal orientation-dependent Casimir interactions between non-spherical colloids in a 2D critical Ising model, combining Monte Carlo simulations with exact analytical results for various boundary conditions.

Contribution

It provides new insights into the orientation-dependent Casimir forces on needles in 2D critical systems, including both numerical and exact analytical results for different geometries and boundary conditions.

Findings

Interaction depends on strip width, needle length, position, and orientation.

Monte Carlo simulations match analytic predictions for small needles.

Exact results are derived for specific geometries and boundary conditions.

Abstract

We investigate the universal orientation-dependent interactions between non-spherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at bulk criticality. For a needle in an Ising strip the interaction on mesoscopic scales depends on the width of the strip and the length, position, and orientation of the needle. By lattice Monte Carlo simulations we evaluate the free energy difference between needle configurations being parallel and perpendicular to the strip. We concentrate on small but nonetheless mesoscopic needle lengths for which analytic predictions are available for comparison. All combinations of boundary conditions for the needles and boundaries are considered which belong to either the "normal" or the "ordinary" surface universality class, i.e., which induce local order or disorder, respectively. We also derive exact results for needles of arbitrary mesoscopic length, in particular for needles embedded in a half plane and oriented perpendicular to the corresponding boundary as well as for needles embedded at the center line of a symmetric strip with parallel orientation.