Ehrenfest Scheme of Higher Dimensional Topological AdS Black Holes in   The Third Order Lovelock-Born-Infeld Gravity
  Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in Lovelock-Born-Infeld gravity. In particular, we give an explicit expression of the universal number \chi=\frac{P_c v_c}{T_c} in terms of the space dimension $n$. Then, we examine the phase transitions at the critical points of such topological black holes for 6 \leq n \leq 11 as required by the physical condition of the thermodynamical quantities. More precisely, the Ehrenfest equations have been checked revealing that the black hole system undergoes a second phase transition at the critical points. 
A. Belhaj, M. Chabab, H. EL Moumni, K. Masmar, M. B. Sedra
hep-th gr-qc