Critical fluctuations and phase transitions in the antiferromagnetic Potts model

The antiferromagnetic Potts model with $q=4, 5, or 6$ states per ion on a simple cubic lattice is studied by Monte Carlo computer experiments which are analyzed by forming a two-ion correlation function and extracting a correlation length to look for critical fluctuations. The $q=5\mathrm{}$ model, previously believed not to order, is shown to undergo a phase transition. The absence of a phase transition for $q=6\mathrm{}$ is confirmed.