Phase transitions and geometrothermodynamics of regular black holes

In this paper we study the thermodynamics and state space geometry of a set of regular black hole solutions such as Bardeen black hole (1968), Ayon-Beato and Garcia black hole (Phys Rev Lett 80: 5056, 1998), Hayward black hole (Phys Rev Lett 96: 031103, 2006) and Berej-Matyjasek-Trynieki-Wornowicz black hole (Gen Relativ Gravit 38(5): 885906, 2006). We find that all these black holes show second order thermodynamic phase transitions by observing discontinuities in heat capacity-entropy graphs as well as the cusp type double point in free energy-temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curvature scalar of the Legendre invariant metric.