  We consider a prototypical system of an infinite range transverse field Ising
model coupled to a bosonic bath. By integrating out the bosonic degrees, an
effective anisotropic Heisenberg model is obtained for the spin system. The
phase diagram of the latter is calculated as a function of coupling to the heat
bath and the transverse magnetic field. Collective excitations at low
temeratures are assessed within a spin-wave like analysis that exhibits a
vanishing energy gap at the quantum critical point. We also consider another
limit where the system reduces to a generalized spin-boson model of two
interacting spins. By increasing the coupling strength with the heat bath, the
two-spin wavefunction changes from an entangled state to a factorized state of
two spins which are aligned along the transverse field. We also discuss the
possible realization and application of the model to different physical
systems.
