EXACT PARTITION FUNCTION FOR THE POTTS MODEL WITH NEXT-NEAREST NEIGHBOR COUPLINGS ON ARBITRARY-LENGTH LADDERS

Abstract

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 Möbius 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 ℬ in the corresponding [Formula: see text] space, arising as the accumulation set of partition function zeros as n → ∞.