Exact partition function for the Potts model with next-nearest neighbor couplings on arbitrary-length ladders

We present exact calculations of partition function Z of the q-state Potts model with next-nearest-neighbor spin -spin couplings, both for the ferromagnetic and antiferromagnetic case, for arbitrary temperature, on n-vertex ladders with free, cyclic, and Mobius longitudinal boundary conditions. The free energy is calculated exactly for the infinite-length limit of these strip graphs and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus a in the corresponding C-2 space, arising as the accumulation set of partition function zeros as n --> infinity.