Thermodynamical Equilibrium of Vortices in the Isotropic Bidimensional Kac Rotator

TL;DR

This paper investigates the thermodynamical equilibrium states of vortices in an isotropic bidimensional Kac rotator, using gradient-flow dynamics to analyze local minima and drawing parallels with the Ginzburg-Landau functional.

Contribution

It introduces a novel analysis of vortex equilibria in the Kac rotator model, highlighting analogies with Ginzburg-Landau theory and addressing the challenges posed by non-weakly closed vorticity conditions.

Findings

Identification of local minima in the Kac functional

Strong analogy with Ginzburg-Landau functional in infinite volume

Insights into vortex configurations under long-range interactions

Abstract

We consider here the problem of extrema for the Kac functional with long range, ferromagnetic interaction, and vorticity conditions at infinity which make it not weakly closed. Using a gradient-flow dynamics, we investigate local minima, showing strong analogies with the Ginzburg-Landau functional in infinite volume.