Phase transitions and Geometrothermodynamics of Regular black holes

Abstract: In this paper we study the thermodynamics and state space geometry of regular black hole solutions such as Bardeen black hole, Ay\'{o}n-Beato and Garc\'{i}a black hole, Hayward black hole and Berej-Matyjasek-Trynieki-Wornowicz black hole. We find that all these black holes show second order thermodynamic phase transitions(SOTPT) 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.