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

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  • Chang, Shu-Chiuan
  • Shrock, Robert

Abstract

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

Suggested Citation

  • Chang, Shu-Chiuan & Shrock, Robert, 2001. "Ground state entropy of the Potts antiferromagnet on strips of the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 290(3), pages 402-430.
    • Handle: RePEc:eee:phsmap:v:290:y:2001:i:3:p:402-430
    DOI: 10.1016/S0378-4371(00)00457-X
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