Critical Casimir Force between Inhomogeneous Boundaries

TL;DR

This paper investigates the critical Casimir force between inhomogeneous boundaries in a binary mixture, revealing a boundary-induced phase transition that causes a sign change in the force and diverging correlation length, analyzed via conformal field theory.

Contribution

It introduces a theoretical framework combining conformal field theory and Majorana fermion mapping to analyze the universal scaling function of the Casimir force crossover.

Findings

Identification of a boundary-induced phase transition affecting the Casimir force

Derivation of the universal scaling function for the force crossover

Prediction of a sign change in the Casimir force at the transition

Abstract

To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.