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arXiv · 2411.00423

Geometric properties of the additional third-order transitions in the two-dimensional Potts model

Wei Liu·Xin Zhang·Lei Shi·Kai Qi·Xiang Li·Fangfang Wang·Zengru Di
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Abstract

Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the $q$-state Potts model (for $q \geq 3$), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of $q$. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for $q = 6$ and $q = 8$, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach.

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Wei Liu, Xin Zhang, Lei Shi, Kai Qi, Xiang Li, Fangfang Wang, Zengru Di. 2024-11-01. Geometric properties of the additional third-order transitions in the two-dimensional Potts model. https://arxiv.org/abs/2411.00423

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