Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls

TL;DR

This paper investigates the lateral critical Casimir force in a 2D Ising strip with inhomogeneous walls, analyzing its behavior near the critical point and its relation to magnetization profiles and bridge formation.

Contribution

It provides an exact analysis of the lateral Casimir force in a 2D Ising model with inhomogeneous walls, linking force properties to magnetization morphologies and bridge breaking.

Findings

Lateral Casimir force exhibits scaling near the critical point.

Magnetization profiles show bridge formation between inhomogeneities.

Breaking of the bridge correlates with inflection points in the force.

Abstract

We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width $M$. The inhomogeneity of each of the walls has size $N_1$; they are shifted by the distance $L$ along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters $M$, $N_1$, $L$. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force.