Criticality versus q in the (2+1)-dimensional Zq clock model

Using Monte Carlo simulations we have studied the d=3 Z(q) clock model in two different representations, the phase representation and the loop-gas/dumbbell-gas representation. We find that for q> or =5 the critical exponents alpha and nu for the specific heat and the correlation length, respectively, take on values corresponding to the case q--> infinity, the XY model. Hence in terms of critical properties the limiting behavior is reached already at q=5.