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Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: A graph-convolutional transfer-learning study |
| Zheng Zhou(周政)1,†, Xu-Yang Hou(侯旭阳)1,†, and Hao Guo(郭昊)1,2,‡ |
1 School of Physics, Southeast University, Jiulonghu Campus, Nanjing 211189, China;
2 Hefei National Laboratory, Hefei 230088, China |
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Abstract We investigate the ferromagnetic $q$-state Potts model on spherical Fibonacci graphs. These graphs are constructed by embedding quasi-uniform sites on a sphere and defining interactions via a chord-distance cutoff chosen so as to yield a network approximating four-neighbor connectivity. By combining Swendsen-Wang cluster Monte Carlo simulations with graph convolutional networks (GCNs), which operate directly on the adjacency structure and node spins, we develop a unified phase-classification framework applicable to both regular planar lattices and curved, irregular spherical graphs. Benchmarks on planar lattices demonstrate an efficient transfer strategy: after a fixed binarization of Potts spins into an effective Ising variable, a single GCN pre-trained on the Ising model can localize the transition region for different $q$ values without retraining. Applying this strategy to spherical graphs, we find that curvature- and defect-induced connectivity irregularities induce only modest shifts in the inferred transition temperatures relative to their planar counterparts. Further analysis shows that the curvature-induced shift of the critical temperature is most pronounced at small $q$ and diminishes rapidly as $q$ increases. This trend is consistent with the physical picture that, in two dimensions, the Potts model undergoes a transition from a continuous phase transition to a weakly first-order one for $q$>4, accompanied by a pronounced reduction in the correlation length.
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Received: 13 February 2026
Revised: 22 April 2026
Accepted manuscript online: 29 April 2026
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PACS:
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05.50.+q
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(Lattice theory and statistics)
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64.60.Cn
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(Order-disorder transformations)
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02.70.Uu
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(Applications of Monte Carlo methods)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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| Fund: Project supported by the Innovation Program for Quantum Science and Technology-National Science and Technology Major Project (Grant No. 2021ZD0301904), the National Natural Science Foundation of China (Grant No. 12447216), and the National Natural Science Foundation of China (Grant No. 12405008). |
Corresponding Authors:
Hao Guo
E-mail: guohao.ph@seu.edu.cn
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Cite this article:
Zheng Zhou(周政), Xu-Yang Hou(侯旭阳), and Hao Guo(郭昊) Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: A graph-convolutional transfer-learning study 2026 Chin. Phys. B 35 070505
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