  Phase transitions in charged topological black holes dressed with a scalar
field are studied. These black holes are solutions of the Einstein-Maxwell
theory with a negative cosmological constant and a conformally coupled real
self-interacting scalar field. Comparing, in the grand canonical ensemble, the
free energies of the hairy and undressed black holes two different phase
transitions are found. The first of them is one of second-order type and it
occurs at a temperature defined by the value of the cosmological constant.
Below this temperature an undressed black hole spontaneously acquires a scalar
hair. The other phase transition is one of first-order type. The corresponding
critical temperature, which is bounded from above by the one of the previous
case, strongly depends on the coupling constant of the quartic self-interaction
potential, and this transition only appears when the coupling constant is less
than a certain value. In this case, below the critical temperature the
undressed black is thermodynamically favored. However, when the temperature
exceeds the critical value a hairy black hole is likely to be occur.
