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

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