Universality of the complete-graph Potts model with $0< q \leq 2$
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| Format: | Preprint |
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2025
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| _version_ | 1866911037715906560 |
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| author | Peng, Zirui Fang, Sheng Hu, Hao Deng, Youjin |
| author_facet | Peng, Zirui Fang, Sheng Hu, Hao Deng, Youjin |
| contents | Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of microscopic details. In a simplest and mean-field treatment--i.e., the Potts model on complete graph (CG), the phase transition is further established to be of percolation universality for the range of $0 < q <2$. By simulating the CG Potts model in the random-cluster representation, we numerically demonstrate such a hyper-universality that the critical exponents are the same for $0< q <2$ and, moreover, the Ising system ($q = 2$) exhibits a variety of critical geometric properties in percolation universality. On the other hand, many other universal properties in the finite-size scaling (FSS) theory, including Binder-like ratios and distribution function of the order parameter, are observed to be $q$-dependent. Our finding provides valuable insights for the study of critical phenomena in finite spatial dimensions, particularly when the FSS theory is utilized. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of the complete-graph Potts model with $0< q \leq 2$ Peng, Zirui Fang, Sheng Hu, Hao Deng, Youjin Statistical Mechanics Computational Physics Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of microscopic details. In a simplest and mean-field treatment--i.e., the Potts model on complete graph (CG), the phase transition is further established to be of percolation universality for the range of $0 < q <2$. By simulating the CG Potts model in the random-cluster representation, we numerically demonstrate such a hyper-universality that the critical exponents are the same for $0< q <2$ and, moreover, the Ising system ($q = 2$) exhibits a variety of critical geometric properties in percolation universality. On the other hand, many other universal properties in the finite-size scaling (FSS) theory, including Binder-like ratios and distribution function of the order parameter, are observed to be $q$-dependent. Our finding provides valuable insights for the study of critical phenomena in finite spatial dimensions, particularly when the FSS theory is utilized. |
| title | Universality of the complete-graph Potts model with $0< q \leq 2$ |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2501.16930 |