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

We study the ground state degeneracy per site (exponent of the ground state entropy) $W(\mathrm{\Lambda },(L_x=\mathrm{\infty })\times L_y,q)$ for the $q$-state Potts antiferromagnet on infinitely long strips with width $L_y$ of 2D lattices $\mathrm{\Lambda }$ 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 $L_y\simeq 4$, $W(\mathrm{\Lambda },(L_x=\mathrm{\infty })\times L_y,q)$ is within about 5 % and $\mathcal{O}({10}^{-3})$ of the 2D value $W(\Lambda,(L_x=\infty) \times (L_y=\infty),q)$forFBC$_y$andPBC$_y$,respectively\mathrm{.}Theapproachof$W$ 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.