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

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