General structural results for Potts model partition functions on lattice strips

We present a set of general results on structural features of the q-state Potts model partition function Z(G,q,v) for arbitrary q and temperature Boltzmann variable v for various lattice strips of arbitrarily great width L_y vertices and length L_x vertices, including (i) cyclic and Möbius strips of the square and triangular lattices, and (ii) self-dual cyclic strips of the square lattice. We also present an exact solution for the chromatic polynomial for the cyclic and Möbius strips of the square lattice with width L_y=5 (the greatest width for which an exact solution has been obtained so far for these families). In the L_x→∞ limit, we calculate the ground-state degeneracy per site, W(q) and determine the boundary ℬ across which W(q) is singular in the complex q plane.