  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.
