Ground state entropy of the Potts antiferromagnet on strips of the square lattice

We present exact solutions for the zero-temperature partition function (chromatic polynomial P) and the ground state degeneracy per site W (= exponent of the ground-state entropy) for the q-state Potts antiferromagnet on strips of the square lattice of width Ly vertices and arbitrarily great length Lx vertices. The specific solutions are for (a) Ly=4, (FBCy,PBCx) (cyclic); (b) Ly=4,(FBCy,TPBCx) (Möbius); (c) Ly=5,6,(PBCy,FBCx) (cylindrical); and (d) Ly=5, (FBCy,FBCx) (open), where FBC, PBC, and TPBC denote free, periodic, and twisted periodic boundary conditions, respectively. In the Lx→∞ limit of each strip we discuss the analytic structure of W in the complex q plane. The respective W functions are evaluated numerically for various values of q. Several inferences are presented for the chromatic polynomials and analytic structure of W for lattice strips with arbitrarily great Ly. The absence of a nonpathological Lx→∞ limit for real nonintegral q in the interval 0