  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>5 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.
