Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

Abstract

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (Möbius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0>0$. The chromatic zeros and their accumulation set $\mathcal{B}$ exhibit the rather unusual property of including support for $Re(q)<0$ and provide further evidence for a relevant conjecture.

Comments: 7 pages, Latex, 4 figs., J. Phys. A Lett., in press