Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study
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arXiv
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| Format: | Preprint |
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2026
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| author | Zhou, Zheng Hou, Xu-Yang Guo, Hao |
| author_facet | Zhou, Zheng Hou, Xu-Yang Guo, Hao |
| contents | 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 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 pretrained 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 produce only modest shifts in the inferred transition temperatures relative to planar baselines. 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 of the correlation length. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_07346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study Zhou, Zheng Hou, Xu-Yang Guo, Hao Statistical Mechanics Computational Physics 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 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 pretrained 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 produce only modest shifts in the inferred transition temperatures relative to planar baselines. 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 of the correlation length. |
| title | Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2601.07346 |