Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

TL;DR

This paper provides exact calculations of the ground-state entropy for the Potts antiferromagnet on cyclic strip graphs, revealing complex analytic properties and supporting conjectures about chromatic zeros.

Contribution

It introduces exact solutions for the zero-temperature partition function and ground-state entropy on cyclic and M"obius strip graphs, and explores their complex analytic structure.

Findings

Chromatic zeros include support for Re(q) < 0

Identification of the maximal region for analytic continuation of S_0

Evidence supporting conjectures about chromatic zeros and accumulation sets

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 (M\"obius) 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 ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.