  We use Monte Carlo simulations to study chains of Ising- and XY-spins with
dissipation coupling to the site variables. The phase diagram and critical
exponents of the dissipative Ising chain in a transverse magnetic field have
been computed previously, and here we consider a universal ratio of
susceptibilities. We furthermore present the phase diagram and exponents of the
dissipative XY-chain, which exhibits a second order phase transition. All our
results compare well with the predictions from a dissipative $\phi^4$ field
theory.
