  Using large-scale Monte Carlo computations, we study two versions of a
$(1+1)D$ $Z_4$-symmetric model with Ohmic bond dissipation. In one of these
versions, the variables are restricted to the interval $[0,2\pi>$, while the
domain is unrestricted in the other version. The compact model features a
completely ordered phase with a broken $Z_4$ symmetry and a disordered phase,
separated by a critical line. The noncompact model features three phases. In
addition to the two phases exhibited by the compact model, there is also an
intermediate phase with isotropic quasi-long-range order. We calculate the
dynamical critical exponent $z$ along the critical lines of both models to see
if the compactness of the variable is relevant to the critical scaling between
space and imaginary time. There appears to be no difference between the two
models in that respect, and we find $z\approx1$ for the single phase transition
in the compact model as well as for both transitions in the noncompact model.
