  Using Monte Carlo simulations we have studied the $d=3$ $Z_q$ clock model in
two different representations, the phase-representation and the
loop/dumbbell-gas (LDG) representation. We find that for $q \ge 5$ the critical
exponents $\alpha$ and $\nu$ for the specific heat and the correlation length,
respectively, take on values corresponding to the case $q\to \infty$, where
$\lim_{q \to \infty} Z_q = 3DXY$ model, i.e. in terms of critical properties
the limiting behaviour is reached already at $q=5$.
