Zeros of the Potts Model Partition Function on Sierpinski Graphs

We calculate zeros of the $q$-state Potts model partition function on $m$’th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m\to \mathrm{\infty }$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_{\mathrm{\infty }}$.