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 L_y vertices and arbitrarily great length L_x vertices. The specific solutions are for (a) L_y = 4, (FBC_y, PBC_x) (cyclic); (b) L_y = 4, (FBC_y, TPBC_x) (Mobius); (c) L_y = 5,6, (PBC_y, FBC_x) (cylindrical); and (d) L_y = 5, (FBC_y, FBC_x) (open), where FBC, PBC, and TPBC denote free, periodic, and twisted periodic boundary conditions, respectively. In the L_x→∞ 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 L_y. The absence of a nonpathological L_x→∞ limit for real nonintegral q in the interval 0<q<3 (0<q<4) for strips of the square (triangular) lattice is discussed.