T=0 Partition Functions for Potts Antiferromagnets on Moebius Strips and Effects of Graph Topology

TL;DR

This paper provides exact calculations of the zero-temperature partition function for Potts antiferromagnets on Moebius strips, analyzing how graph topology influences these functions compared to periodic boundary conditions.

Contribution

It introduces exact solutions for Potts antiferromagnets on Moebius strips with specific widths, highlighting the effects of topology on partition functions.

Findings

Exact partition functions for Moebius strips with L_y=2,3

Comparison with periodic boundary condition cases

Insights into topology's effect on graph properties

Abstract

We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently the chromatic polynomial) for Moebius strips, with width $L_y=2$ or 3, of regular lattices and homeomorphic expansions thereof. These are compared with the corresponding partition functions for strip graphs with (untwisted) periodic longitudinal boundary conditions.