Partition function zeros of a restricted Potts model on self-dual strips of the square lattice

We calculate the partition function Z(G, Q, v) of the Q-state Potts model exactly for self-dual cyclic square-lattice strips of various widths L _y and arbitrarily large lengths L_x, with Q and v restricted to satisfy the relation Q = v². From these calculations, in the limit L_x → ∞, we determine the continuous accumulation locus Β of the partition function zeros in the v and Q planes. A number of interesting features of this locus are discussed and a conjecture is given for properties applicable to arbitrarily large width. Relations with the loci Β for general Q and v are analyzed.