Large-q series expansion for the ground state degeneracy of the q-state Potts antiferromagnet on the (3.12^2) lattice

TL;DR

This paper derives a large-q series expansion for the ground state degeneracy of the q-state Potts antiferromagnet on a specific lattice, revealing a strong agreement with recent theoretical bounds.

Contribution

It provides the first detailed large-q series expansion for this lattice's ground state degeneracy, extending to order 19 in the expansion parameter.

Findings

Series expansion matches rigorous lower bounds up to order 18.

Provides new quantitative insights into the ground state entropy.

Enhances understanding of Potts antiferromagnet properties on complex lattices.

Abstract

We calculate the large-$q$ series expansion for the ground state degeneracy (= exponent of the ground state entropy) per site of the $q$-state Potts antiferromagnet on the $(3 \cdot 12^2)$ lattice, to order $O(y^{19})$, where $y=1/(q-1)$. We note a remarkable agreement, to $O(y^{18})$, between this series and a rigorous lower bound derived recently.