Extended phase space thermodynamics for third-order Lovelock black holes in diverse dimensions

Treating the cosmological constant as thermodynamic pressure and its conjugate as thermodynamic volume, we investigate the critical behavior of the third-order Lovelock black holes in diverse dimensions. For black hole horizons with different normalized sectional curvature k = 0, +/- 1, the corresponding critical behaviors differ drastically. For k = 0, there is no critical point in the extended thermodynamic phase space. For k = -1, there is a single critical point in any dimension d >= 7, and for k = +1, there is a single critical point in 7 dimensions and two critical points in 8, 9, 10, 11 dimensions. We studied the corresponding phase structures in all possible cases.