  We study the zero temperature static properties of dissipative ensembles of
quantum Ising spins arranged on periodic one dimensional finite clusters and on
an infinite chain. The spins interact ferro-magnetically with nearest-neighbour
pure and random couplings. They are subject to a transverse field and coupled
to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system
using Monte Carlo simulations of the classical two-dimensional counterpart
model. The coupling to the bath enhances the extent of the ordered phase, as
found in mean-field spin-glasses. In the case of finite clusters we show that a
generalization of the Caldeira-Leggett localization transition exists. In the
case of the infinite random chain we study the effect of dissipation on the
transition and the Griffiths phase.
