Phase transitions of magnetic AdS4 black holes with scalar hair

We determine the thermodynamic properties of a class of spherically symmetric and static black holes in AdS(4) with magnetic charges and scalar hair. These black holes are solutions in four-dimensional N = 2 gauged supergravity that can arise from 11-dimensional supergravity compactified on S-7. At zero temperature, they preserve supersymmetry and hence are stable. At nonzero temperatures, we explore in detail the canonical ensemble and stability of solutions and find a first-order phase transition between small and large hairy black holes. The transition emerges as a liquid-gas phase transition in the dual three-dimensional field theory on R x S-2 with magnetic flux through S-2.