Partition function zeros of a restricted Potts model on lattice strips and effects of boundary conditions

We calculate exactly the partition function Z(G, Q, v) of the Q-state Potts model with temperature-like Boltzmann variable v for strip graphs G of the square and triangular lattices of various widths L_y and arbitrarily great lengths L_x, with a variety of boundary conditions, and with Q and v restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit L_x → ∞, we determine the continuous accumulation loci of the partition function zeros in the v and Q planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.