Properties of theq-state clock model forq=4, 5, and 6

The two-dimensional clock models for $q=4, 5, \mathrm{and} 6$ were simulated on lattices of size 256 and 1024. Various properties were computed including the specific heat, susceptibility, vorticity, and correlation times. However, only a Monte Carlo renormalization-group analysis was capable of locating quantitatively the phase transitions for $q=5\mathrm{} \mathrm{and} 6$. The results agree with the qualitative picture obtained for the Villain version of the clock model. The relevance of this work to the two-dimensional melting problem is discussed. MS code no. BT2080 1977