dorsal/arxiv
View SchemaCurvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study
| Authors | Zheng Zhou, Xu-Yang Hou, Hao Guo |
|---|---|
| Categories | |
| ArXiv ID | 2601.07346vv1 |
| URL | https://arxiv.org/abs/2601.07346 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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 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.
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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 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 $q\u003e4$, accompanied by a pronounced reduction of the correlation length.",
"arxiv_id": "2601.07346",
"authors": [
"Zheng Zhou",
"Xu-Yang Hou",
"Hao Guo"
],
"categories": [
"cond-mat.stat-mech",
"physics.comp-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study",
"url": "https://arxiv.org/abs/2601.07346",
"version": "v1"
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