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 great lengths $L_x$, with $Q$ and $v$ restricted to satisfy the relation $Q=v^2$. From these calculations, in the limit $L_x\to \mathrm{\infty }$, we determine the continuous accumulation locus $\mathcal{B}$ 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 for arbitrarily great width. Relations with the loci $\mathcal{B}$ for general $Q$ and $v$ are analyzed.