Heisenberg Spins on a Cylinder Section

TL;DR

This paper investigates classical Heisenberg spins on a finite elastic cylinder section, revealing topological solitons, geometric frustration, and a novel shrinking effect due to elastic deformations.

Contribution

It introduces a continuum elastic model for spins on a finite cylinder, uncovering new geometric effects and soliton configurations influenced by elasticity and boundary conditions.

Findings

Existence of topological solitons on finite cylinders

Elastic deformations cause a global shrinking of the cylinder

Inhomogeneous Lamé equation describes shape relaxation

Abstract

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lam\'e equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.