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arXiv · 2312.05414

Fisher zeros and critical behavior for the Ising model on Sierpinski gasket

Shaosong Liu
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Abstract

In this paper, we provide a proof of the explicit formula for the partition function of the Ising model on the Sierpinski gasket. Additionally, we demonstrate the dynamic behavior of the zero distribution of the partition function when a sequence of appropriate regions is selected. Through this analysis, it is shown that the density of zeros around temperature $0$ exponentially diminishes at a rate of $\frac{1}{3^n}$, and the pressure function approaches the logarithmic function.

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Shaosong Liu. 2024-06-02. Fisher zeros and critical behavior for the Ising model on Sierpinski gasket. https://arxiv.org/abs/2312.05414

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