Ehrenfest's scheme and thermodynamic geometry in Born-Infeld AdS black   holes
  In this paper we analyze the phase transition phenomena in Born-Infeld AdS black holes using Ehrenfest's scheme of standard thermodynamics. The critical points are marked by the divergences in the heat capacity. In order to investigate the nature of the phase transition, we analytically check both the Ehrenfest's equations near the critical points. Our analysis reveals that this is indeed a second order phase transition. Finally, we analyze the nature of the phase transition using state space geometry approach. This is found to be compatible with the Ehrenfest's scheme. 
Arindam Lala, Dibakar Roychowdhury
gr-qc hep-th