Phases of higher spin black holes: Hawking-Page, transitions between black holes, and a critical point

We study the thermodynamic phase diagram of three-dimensional sl(N;R) higher spin black holes. By analyzing the semiclassical partition function we uncover a rich structure that includes Hawking-Page transitions to the AdS3 vacuum, first order phase transitions among black hole states, and a second order critical point. Our analysis is explicit for N=4 but we extrapolate some of our conclusions to arbitrary N. In particular, we argue that even N is stable in the ensemble under consideration but odd N is not.