Zeros of the Potts Model Partition Function on Sierpinski Graphs

Shu-Chiuan Chang; Robert Shrock

doi:10.1016/j.physleta.2013.01.017

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arXiv · 1209.0020

Zeros of the Potts Model Partition Function on Sierpinski Graphs

Shu-Chiuan Chang·Robert Shrock

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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, $S_\infty$.

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Shu-Chiuan Chang, Robert Shrock. 2012-08-31. Zeros of the Potts Model Partition Function on Sierpinski Graphs. https://doi.org/10.1016/j.physleta.2013.01.017

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