Vortices and Magnetization in Kac's Model

TL;DR

This paper investigates vortex structures and magnetization in a 2D ferromagnetic Kac model, revealing vortex minimizers with features similar to Ginzburg-Landau vortices through numerical analysis.

Contribution

It provides the first numerical evidence of vortex minimizers in a Kac potential model, connecting microscopic interactions with macroscopic vortex phenomena.

Findings

Vortex structures are present in the minimizers of the free energy.

Minimizers exhibit features similar to Ginzburg-Landau vortices.

Numerical evidence supports the existence of vortex configurations in the model.

Abstract

We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with compact support. The system is subject to boundary conditions with vorticity. Using a Glauber like dynamics, we compute minimizers of the free energy functional at low temperature, i.e. in the regime of phase transition. We have the numerical evidence of a vortex structure for minimizers, which present many common features with those of the Ginzburg-Landau functional.