Casimir interactions in Ising strips with boundary fields: exact results

TL;DR

This paper derives exact expressions for critical Casimir forces in Ising strips with boundary fields, showing how temperature and fields influence force magnitude and sign, and proposes a systematic approach for broader models.

Contribution

It provides an exact statistical mechanical derivation of Casimir forces in Ising strips with arbitrary boundary fields, introducing a linked cluster expansion method.

Findings

Force strength and sign can be controlled by temperature and boundary fields.

The derivation uses a linked cluster expansion for interpretation.

The approach can be extended to more general models.

Abstract

An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for deriving the critical Casimir force which can be used in more general models.