Heisenberg Spins on an Elastic Torus Section

TL;DR

This paper investigates classical Heisenberg spins on an elastic torus section, revealing how elastic deformations influence topological solitons and induce a global shrinking with swellings due to geometric frustration.

Contribution

It introduces a model combining spin configurations with elastic deformations, deriving an inhomogeneous Lamé equation and uncovering a new geometric effect of global shrinking.

Findings

Topological solitons are affected by torus eccentricity.

Elastic deformations lead to inhomogeneous shapes of the torus.

A novel geometric effect of global shrinking with swellings is identified.

Abstract

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic torus section with homogeneous boundary conditions. The corresponding rigid model exhibits topological soliton configurations with geometrical frustration due to the torus eccentricity. 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 with swellings.