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.
Highlights
The interest in the O(3)-sigma model arises from the description of cosmic strings [1,2,3] as well as phenomena in condensed matter physics [4]
This result, is unlike the results presented in braneworld scenarios, and due to the configurational entropy profile of the O(3)-sigma model, our model does not support multiple phase transitions
By choosing a self-interaction logarithmic potential with symmetry breaking in the O(3)sigma model gauged with the Maxwell gauge fields, we get purely neutral magnetic vortices
Summary
The interest in the O(3)-sigma model arises from the description of cosmic strings [1,2,3] as well as phenomena in condensed matter physics [4]. Topological solutions of the gauged O(3)-sigma model have been extensively studied [11,17,18,19,20,21,22]. It is interesting to mention that there are several types of topological structures Among these defects, we have the vortices that arise in 3D models [26,27]. To study vortices in our model, we use a technique known as the Bogomol’nyi–Prasad–Sommerfield (BPS) method. We propose an Abelian O(3)-sigma model, governed by a Maxwell term, with a Gausson potential, and show that this model admits topological vortex solutions. It is possible to have other vortex solutions that describe more complex structures with electric and magnetic field flux. From the previous expression, it is clear that the magnetic flux of the vortex is quantized in each topological sector
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