Magnetic charge effects on thermodynamic phase transition of modified anti de Sitter Ayón-Beato-García black holes with five parameters

In this paper, we choose a generalized Ayón-Beato-García (ABG) magnetic charged black hole with five parameters to investigate the possibility of thermodynamic phase transition and coexistence of different gas/liquid/solid phases of this black hole. In fact, this work is an extension of our recent work where ABG black hole with three parameters were used to seek the phase transition. In this work, we obtain other physical values on the parameters with respect to our previous work, where the phase transition happens together with the coexistence point of different phases in the phase space.