Phase Structure of Higher Spin Black Holes

We revisit the study of the phase structure of higher spin black holes
carried out in arXiv:1210.0284 using the "canonical formalism". In
particular we study the low as well as high temperature regimes. We
show that the Hawking-Page transition takes place in the low
temperature regime. The thermodynamically favoured phase changes from
conical surplus to black holes and then again to conical surplus as we
increase temperature. We then show that in the high temperature regime
the diagonal embedding gives the appropriate description. We also give
a map between the parameters of the theory near the IR and UV fixed
points. This makes the "good" solutions near one end map to the "bad"
solutions near the other end and vice versa.