  We consider a one-dimensional Ising model in a transverse magnetic field
coupled to a dissipative heat bath. The phase diagram and the critical
exponents are determined from extensive Monte Carlo simulations. It is shown
that the character of the quantum phase transition is radically altered from
the corresponding non-dissipative model and the double-well coupled to a
dissipative heat bath with linear friction. Spatial couplings and the
dissipative dynamics combine to form a new quantum criticality.
