Exact partition functions for Potts antiferromagnets on cyclic lattice strips

We present exact calculations of the zero-temperature partition function of the q-state Potts antiferromagnet on arbitrarily long strips of the square, triangular, and kagomé lattices with width Ly=2 or 3 vertices and with periodic longitudinal boundary conditions. From these, in the limit of infinite length, we obtain the exact ground-state entropy S0=kB ln W. These results are of interest since this model exhibits nonzero ground-state entropy S0>0 for sufficiently large q and hence is an exception to the third law of thermodynamics. We also include results for homeomorphic expansions of the square lattice strip. The analytic properties of W(q) are determined and related to zeros of the chromatic polynomial for long finite strips