Thermodynamics and geometrothermodynamics of regular black hole with nonlinear electrodynamics

In this paper we investigate the phase transition and geometrothermodynamics of regular electrically charged black hole in nonlinear electrodynamics theory coupled to general relativity. We analyze the types of phase transition of the thermodynamic system by calculating its temperature, heat capacity, and free energy, etc. We find that there are second-order phase transitions from the heat capacity for a large value of S. In addition, employing the geometrothermodynamics, we obtain a Legendre invariance metric and find the relationship between the thermodynamical phase transition and the singularity of the curvature scalar in the regular black hole with the nonlinear electrodynamics.