Thermodynamics and phase transitions of non-linear charged black hole in AdS spacetime

We have derived a non-linear charged black hole solution, in the AdS spacetime, which behaves asymptotically like the RN-AdS black hole but at the short distances like a dS geometry. Thus, the black hole is regular. The thermodynamic quantities of the black hole are derived. Also, we analyzed in details the phase transitions of the black hole by observing the discontinuity of the heat capacity at constant pressure and the cusp type double points in the Gibbs free energy-temperature graph. Furthermore, the thermodynamic phases and their stability are investigated relying on the off-sell Gibbs free energy. Finally, we calculated the critical exponents characterizing the behavior of the relevant thermodynamic quantities near the critical point. (orig.)