The three-state antiferromagnetic Potts model on the simple-cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free-energy difference between the broken-sublattice-symmetry and the permutationally-symmetric sublattice phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.

• Received 3 May 1996

DOI:https://doi.org/10.1103/PhysRevE.54.R5885