Ehrenfest scheme of higher dimensional 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 AdS black holes in Lovelock-Born-Infeld gravity. In particular, we derive an explicit expression of the universal number X = 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 black holes for 6 <= n < 11 as required by the physical condition of the thermodynamical quantities including criticality behaviors. More precisely, the Ehrenfest equations have been checked and they reveal that the black hole system undergoes a second phase transition at the critical points.