  We present a new class of black hole solutions with minimally coupled scalar
field in the presence of a negative cosmological constant. We consider a
one-parameter family of self-interaction potentials parametrized by a
dimensionless parameter $g$. When $g=0$, we recover the conformally invariant
solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing $g$
signals the departure from conformal invariance. All solutions are
perturbatively stable for negative black hole mass and they may develop
instabilities for positive mass. Thermodynamically, there is a critical
temperature at vanishing black hole mass, where a higher-order phase transition
occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch
of hairy solutions which undergo a first-order phase transition at a second
critical temperature which depends on $g$ and it is higher than the MTZ
critical temperature. As $g\to 0$, this second critical temperature diverges.
