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

Дата и время публикации : 1997-06-16T18:13:16Z

Авторы публикации и институты :
Robert Shrock (Institute for Theoretical Physics, State University of New York at Stony Brook)
Shan-Ho Tsai (Institute for Theoretical Physics, State University of New York at Stony Brook)

Ссылка на журнал-издание: Phys. Rev. E56, 2733 (1997)
Коментарии к cтатье: 13 pages, Latex, to appear in Phys. Rev. E
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech, hep-lat, math.CO

Краткий обзор статьи: 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.

Category: Physics