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 $W(\mathrm{sq},q)$ 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 $W(\mathrm{sq},q).\mathrm{}$ Similar results are given for the kagomé lattice.

• Received 25 February 1999

DOI:https://doi.org/10.1103/PhysRevE.60.3512