Ground-state degeneracy of Potts antiferromagnets: cases with noncompact W boundaries having multiple points at 1/q=0

摘要

We present exact calculations of the zero-temperature partition function, Z(G, q, T = 0), and ground-state degeneracy (per site), W([G},q), for the q-state Potts antiferromagnet on a number of families of graphs {G} for which the boundary B of regions of analyticity of W in the complex q-plane is noncompact and has the properties that (i) in the z = 1/q-plane, the point z = 0 is a multiple point on B and (ii) B includes support for Re(q) < 0. These families are generated by the method of homeomorphic expansion. Our results give further insight into the conditions for the validity of large-q series expansions for the reduced function W-red = q(-1)W. [References: 37]