Monte-Carlo Simulations of High-q Anti-ferromagnetic Potts Models

Using a highly efficient cluster-flip Monte-Carlo algorithm$^{1}$, we have investigated the ordering in the five- and the six-state anti-ferromagnetic Potts models on a simple cubic lattice. Using a method developed previously$^{2 }$to examine in detail the distribution of spins on sublattices, we show that the five-state case has a phase transition only at zero temperature, and that the six-state case is disordered at all temperatures. $^{1}$ R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987). $^{2}$ S. Rahman, E. Rush and R.H. Swendsen, Phys. Rev. \underline {B58}, 9125 (1998). * present address: Dept. of Materials Science and Engineering, Virginia Tech, VA, USA