Reentrant phase transitions in rotating anti-de Sitter black holes

We study the thermodynamics of higher-dimensional singly spinning asymptotically AdS black holes in the canonical (fixed J) ensemble of extended phase space, where the cosmological constant is treated as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Along with the usual small/large black hole phase transition, we find a new phenomenon of reentrant phase transitions for all d >= 6 dimensions, in which a monotonic variation of the temperature yields two phase transitions from large to small and back to large black holes. This situation is similar to that seen in multicomponent liquids.