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Condensed Matter > Statistical Mechanics

arXiv:2411.00423 (cond-mat)
[Submitted on 1 Nov 2024 (v1), last revised 4 Nov 2024 (this version, v2)]

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

Authors:Xin Zhang, Wei Liu, Lei Shi, Fangfang Wang, Kai Qi, 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>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.
Comments: 12 pages, 8 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:2411.00423 [cond-mat.stat-mech]
  (or arXiv:2411.00423v2 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.2411.00423

Submission history

From: Wei Liu [view email]
[v1] Fri, 1 Nov 2024 07:44:25 UTC (4,908 KB)
[v2] Mon, 4 Nov 2024 02:02:25 UTC (4,873 KB)
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