Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

Details Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

1997-06-16

arxiv.org/abs/cond-mat/9706162v1

Phys. Rev. E56, 2733 (1997)

Physics

Condensed Matter

Statistical Mechanics

13 pages, Latex, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.56.2733

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. Remarkably, these agree exactly to all thirteen 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.

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