Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice

TL;DR

This paper derives rigorous lower bounds for the ground state degeneracy of the Potts antiferromagnet on slabs of the simple cubic lattice, bridging the properties of square and cubic lattices.

Contribution

It provides the first rigorous bounds for the ground state entropy of the Potts antiferromagnet on intermediate lattice slabs, connecting 2D and 3D lattice behaviors.

Findings

Lower bounds for $W$ on slabs of the simple cubic lattice.

Comparison with large-$q$ series expansions for square and cubic lattices.

Numerical comparisons validating the bounds.

Abstract

We calculate rigorous lower bounds for the ground state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-$q$ series expansions for the sq and sc lattices and also present numerical comparisons.