Zeros of the Potts Model Partition Function on Sierpinski Graphs

TL;DR

This paper analyzes the zeros of the Potts model partition function on Sierpinski graphs, revealing asymptotic behaviors and their relation to thermodynamic properties of the model on fractal structures.

Contribution

It provides the first detailed calculation of partition function zeros on Sierpinski graphs and explores their asymptotic distribution as the graph iterates grow.

Findings

Zeros' loci exhibit specific asymptotic patterns as graph size increases.

Zeros relate to phase transition properties of the Potts model on fractals.

Insights into thermodynamic behavior of Potts model on Sierpinski gasket.

Abstract

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 $m \to \infty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_\infty$.