Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

TL;DR

This paper computes exact chromatic polynomials for cyclic polygon chain graphs to analyze the ground state entropy of q-state Potts antiferromagnets, revealing properties of nonanalyticities and complex q-plane continuations.

Contribution

It provides new exact calculations of chromatic polynomials for cyclic polygon chain graphs and explores the analytic structure of the ground state entropy in the complex q-plane.

Findings

Exact chromatic polynomials for cyclic polygon chain graphs

Properties of the nonanalytic locus ${\

Evidence for maximal analytic continuation region in complex q-plane

Abstract

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.