  Scalar fields minimally coupled to General Relativity in three dimensions are
considered. For certain families of self-interaction potentials, new exact
solutions describing solitons and hairy black holes are found. It is shown that
they fit within a relaxed set of asymptotically AdS boundary conditions, whose
asymptotic symmetry group coincides with the one for pure gravity and its
canonical realization possesses the standard central extension. Solitons are
devoid of integration constants and their (negative) mass, fixed and determined
by nontrivial functions of the self-interaction couplings, is shown to be
bounded from below by the mass of AdS spacetime. Remarkably, assuming that a
soliton corresponds to the ground state of the sector of the theory for which
the scalar field is switched on, the semiclassical entropy of the corresponding
hairy black hole is exactly reproduced from Cardy formula once nonvanishing
lowest eigenvalues of the Virasoro operators are taking into account, being
precisely given by the ones associated to the soliton. This provides further
evidence about the robustness of previous results, for which the ground state
energy instead of the central charge appears to play the leading role in order
to reproduce the hairy black hole entropy from a microscopic counting.
