Ground State Entropy in Potts Antiferromagnets and Chromatic Polynomials

email: [email protected]. This research was supported in part by the NSF grant PHY-97-22101. Present address for S.-H. Tsai: Dept. of Physics and Astronomy, Univ. of Georgia, Athens, GA 30602. W is an analytic function of q except on a continuous locus B (B may be null, and there may also be isolated singularities of W ). As n → ∞, the locus B forms via coalescence of a subset of zeros of P (G, q). W is determined via (2) in the region R1 reached by analytic continuation from the real q axis for q > χ(G), where χ(G) is the chromatic number of G, i.e., the minimum number of colors needed to color G with the above constraint. In other regions separated from R1 by nonanalytic boundaries comprising B, only |W | can be determined. There is a subtlety in the definition of W , since at certain special points one encounters the noncommutativity of limits [3]