GROUND-STATE ENTROPY OF POTTS ANTIFERROMAGNETS - BOUNDS, SERIES, AND MONTE-CARLO MEASUREMENTS

We report several results concerning W(Lambda,q)=exp(S-O/k(B)), the ex ponent of the ground-state entropy of the Potts antiferromagnet on a l attice h. First, we improve our previous rigorous lower bound on W(hc, q) for the honeycomb (he) lattice and find that it is extremely accura te; it agrees to the first 11 terms with the large-q series for W(hc,q ). Second, we investigate the heteropolygonal Archimedean 4.8(2) latti ce, derive a rigorous lower bound, on W(4.8(2),q), and calculate the l arge-q series for this function to O(y(12)) where y=1/(q-1). Remarkabl y, these agree exactly to all 13 terms calculated. We also report Mont e Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor c ouplings, focusing on the square lattice with next-nearest-neighbor bo nds.