Ground-State Entropy of the Square-Lattice Q-State Potts Antiferromagnet

The problem of nonzero ground-state entropy has been one of the most important subjects in statistical physics, condensed-matter physics, and mathematics. For the square-lattice Q-state Potts antiferromagnets with Q > 2, the ground-states are highly degenerate, and the nonzero ground-state entropies of these models occur without frustration. However, the exact values of the ground-state entropies for the square-lattice Q-state Potts antiferromagnets are not known except for Q = 3. We evaluate the exact integer values for the numbers of antiferromagnetic ground states on L x L square lattices by using the microcanonical transfer matrix (Q <= 10) and the randomcluster transfer matrix (Q > 10) and we estimate the values of the ground-state entropies in the limit L --> infinity.