  We report magnetic susceptibility, specific heat, and neutron scattering
measurements as a function of applied magnetic field and temperature to
characterize the $S=1/2$ quasi-two-dimensional frustrated magnet piperazinium
hexachlorodicuprate (PHCC). The experiments reveal four distinct phases. At low
temperatures and fields the material forms a quantum paramagnet with a 1 meV
singlet triplet gap and a magnon bandwidth of 1.7 meV. The singlet state
involves multiple spin pairs some of which have negative ground state bond
energies. Increasing the field at low temperatures induces three dimensional
long range antiferromagnetic order at 7.5 Tesla through a continuous phase
transition that can be described as magnon Bose-Einstein condensation. The
phase transition to a fully polarized ferromagnetic state occurs at 37 Tesla.
The ordered antiferromagnetic phase is surrounded by a renormalized classical
regime. The crossover to this phase from the quantum paramagnet is marked by a
distinct anomaly in the magnetic susceptibility which coincides with closure of
the finite temperature singlet-triplet pseudo gap. The phase boundary between
the quantum paramagnet and the Bose-Einstein condensate features a finite
temperature minimum at $T=0.2$ K, which may be associated with coupling to
nuclear spin or lattice degrees of freedom close to quantum criticality.
