Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model

TL;DR

This paper investigates topological solutions in a Chern-Simons O(3)-sigma model with a logarithmic potential, analyzing their properties, complexity, and phase transitions using numerical and theoretical methods.

Contribution

It demonstrates the existence of topological solutions in a 3D model with a logarithmic potential and analyzes their complexity and phase transition behavior.

Findings

Topological solutions exist in the model with a logarithmic potential.

The model supports only a single phase transition.

The energy density and magnetic flux of vortex solutions are characterized.

Abstract

Using a spherically symmetric ansatz, we show that the Chern-Simons O(3)-sigma model with a logarithmic potential admits topological solutions. This result is quite interesting since the Gausson-type logarithmic potential only predicted topological solutions in $(1+1)$D models. To accomplish our goal, the Bogomol'nyi-Prasad-Sommerfield (BPS) method is used, to saturate the energy and obtain the BPS equations. Next, we show by the numerical method is the graphical results of the topological fields, as well as, the magnetic field behavior that generates a flux given by $\Phi_{flux}=-\mathcal{Q}/\kappa$ and the energy density of the structures of vortices. On the other hand, we evaluate the measure of the differential configurational complexity (DCC) of the topological structures, by considering the energy density of the vortex. This analysis is important because it will provide us with information about the possible phase transitions associated with the localized structures and it shows that our model only supports the one-phase transition.