Phase transitions in the logarithmic Maxwell O(3)-sigma model

TL;DR

This paper explores topological solutions and phase transitions in a 3D Maxwell O(3)-sigma model with a Gausson potential, revealing vortex structures, magnetic field configurations, and kink-like solutions through numerical analysis.

Contribution

It introduces the existence of topological solutions and phase transitions in the Maxwell O(3)-sigma model with Gausson potential, supported by numerical evidence and analysis of vortex configurations.

Findings

Support for topological solutions in 3D spacetime

Identification of ring-like magnetic field profiles

Infinite set of kink-like solutions related to model parameters

Abstract

We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell's term and subject to a so-called Gausson's self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting configuration of a ring-like profile. To calculate the differential configurational complexity (DCC) of structures, the spatial energy density of the vortex is used. In fact, the DCC is important because it provides us with information about the possible phase transitions associated with the structures located in the Maxwell-Gausson model in 3D. Finally, we note from the DCC profile an infinite set of kink-like solutions associated with the parameter that controls the vacuum expectation value.