Intermediate-temperature ordering in a three-state antiferromagnetic Potts model

We investigate the ordering in a three-state antiferromagnetic Potts model on a simple cubic lattice by using an efficient cluster-flipping Monte Carlo algorithm. By considering the degeneracy due to the sublattices in two different ways, we arrive at two entirely different phases [rotationally symmetric (RS) and permutationally symmetric sublattice (PSS)] for the intermediate temperature region. Each of these phases has been claimed to be the correct phase by different authors in a recent controversy over ordering in this system. We show that the system moves from a broken sublattice symmetry phase at low temperature to the disordered phase by going through the RS phase at intermediate temperature, and that the PSS phase results from taking the sublattice degeneracy into account in an incorrect fashion. [S0163-1829(98)03738-2].