T=0 Partition Functions for Potts Antiferromagnets on Square Lattice   Strips with (Twisted) Periodic Boundary Conditions
  We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graphs of the square lattice with periodic boundary conditions in the transverse direction and (i) periodic (ii) twisted periodic boundary conditions in the longitudinal direction, so that the strip graphs are embedded on a (i) torus (ii) Klein bottle. In the limit of infinite length, we calculate the exponent of the entropy, W(q), show it to be the same for (i) and (ii), and determine its analytic structure. 
Norman Biggs (CDAM, London School of Economics) and Robert Shrock   (YITP, State Univ. of New York at Stony Brook)