  In this paper, we study ergodic features of invariant measures for the
partially hyperbolic horseshoe at the boundary of uniformly hyperbolic
diffeomorphisms constructed in \cite{DHRS07}. Despite the fact that the
non-wandering set is a horseshoe, it contains intervals. We prove that every
recurrent point has non-zero Lyapunov exponents and all ergodic invariant
measures are hyperbolic. As a consequence, we obtain the existence of
equilibrium measures for any continuous potential. We also obtain an example of
a family of $C^\infty$ potentials with phase transition.
