Ground State Entropy and the q=3 Potts Antiferromagnet on the Honeycomb Lattice

We study the $q$-state Potts antiferromagnet with $q=3$ on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all $T \ge 0$. We also calculate the ground state entropy to be $S_0/k_B = 0.507(10)$ and discuss this result.