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) (Mobius); (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<q<3 (0<q<4) for strips of the square (triangular) lattice is discussed.
|Number of pages||29|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2001 Feb 15|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics