Ground-state entropy of potts antiferromagnets: Bounds, series, and monte carlo measurements

We report several results concerning [Formula Presented] the exponent of the ground-state entropy of the Potts antiferromagnet on a lattice Λ. First, we improve our previous rigorous lower bound on [Formula Presented] for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first 11 terms with the large-[Formula Presented] series for [Formula Presented] Second, we investigate the heteropolygonal Archimedean [Formula Presented] lattice, derive a rigorous lower bound, on [Formula Presented] and calculate the large-[Formula Presented] series for this function to [Formula Presented] where [Formula Presented] Remarkably, these agree exactly to all 13 terms calculated. We also report Monte Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor couplings, focusing on the square lattice with next-nearest-neighbor bonds.