Ground-state degeneracy of Potts antiferromagnets on two-dimensional lattices: approach using infinite cyclic strip graphs.

The q-state Potts antiferromagnet on a lattice Lambda exhibits nonzero ground-state entropy S0=kB 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 kagomé lattice.