Riemannian 2-D conical geometry of Heisenberg ferromagnets

TL;DR

This paper presents an exact 2D Riemannian conical geometry solution for a shear-free Heisenberg ferromagnet within Einstein's equations, analyzing geodesics of magnetic monopoles around it.

Contribution

It introduces a novel conical Riemannian defect solution modeling a ferromagnet in Einstein's framework, linking magnetic and geometric properties.

Findings

Exact conical defect solution in 3D Einstein equations

Geodesic analysis of magnetic monopoles around the ferromagnet

Connection between ferromagnetic properties and Riemannian geometry

Abstract

An exact 2-dimensional conical Riemannian defect solution of 3-dimensional Euclidean Einstein equations of stresses and defects representing a shear-free Heisenberg ferromagnet is given.The system is equivalent to the Einstein equations in vacuum.Geodesics of magnetic monopoles around the ferromagnet are also investigated.