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

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