arXiv:cond-mat/9808057·v2·Statistical Mechanics

Ground State Entropy of Potts Antiferromagnets and the Approach to the 2D Thermodynamic Limit

R. Shrock · S.-H. Tsai

Abstract

We study the ground state degeneracy per site (exponent of the ground state entropy) $W (Λ, (L_{x} = \infty) \times L_{y}, q)$ for the $q$ -state Potts antiferromagnet on infinitely long strips with width $L_{y}$ of 2D lattices $Λ$ with free and periodic boundary conditions in the $y$ direction, denoted FBC $_{y}$ and PBC $_{y}$ . We show that the approach of $W$ to its 2D thermodynamic limit as $L_{y}$ increases is quite rapid; for moderate values of $q$ and $L_{y} ≃ 4$ , $W (Λ, (L_{x} = \infty) \times L_{y}, q)$ is within about 5 % and $O (1 0^{- 3})$ of the 2D value $W (Λ, (L_{x} = \infty) \times (L_{y} = \infty), q)$ for FBC $_{y}$ and PBC $_{y}$ , respectively. The approach of $W$ to the 2D thermodynamic limit is proved to be monotonic (non-monotonic) for FBC $_{y}$ (PBC $_{y}$ ). It is noted that ground state entropy determinations on infinite strips can be used to obtain the central charge for cases with critical ground states.

Comments: 21 pages, Latex, 1 figures; some misprints in Table 1 corrected