Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs

TL;DR

This paper calculates the ground state degeneracy of Potts antiferromagnets on two-dimensional lattices using infinite cyclic strip graphs, providing exact results for square and kagome lattices.

Contribution

It introduces an exact method to compute the ground state degeneracy for Potts antiferromagnets on infinite strip graphs of 2D lattices, addressing a longstanding challenge.

Findings

Exact calculation of W for square lattice strip

Results for kagome lattice

Embodies expected analytic properties of W

Abstract

The q-state Potts antiferromagnet on a lattice $\Lambda$ exhibits nonzero ground state entropy $S_0=k_B \ln W$ for sufficiently large q and hence is an exception to the third law of thermodynamics. An outstanding challenge has been the calculation of W(sq,q) on the square (sq) lattice. We present here an exact calculation of W on an infinite-length cyclic strip of the square lattice which embodies the expected analytic properties of W(sq,q). Similar results are given for the kagom\'e lattice.