Year: 2025
Type: article
Abstract: We investigate the Ising model on a spherical surface, utilizing a Fibonacci lattice to approximate uniform coverage. This setup poses challenges in achieving consistent lattice distribution across the sphere for comparison with planar models. We employ Monte Carlo simulations, principal component analysis, graph convolutional networks (GCNs) to study spin configurations across a range of temperatures and to determine phase transition temperatures. The Fibonacci lattice, despite its uniformity, contains irregular sites that influence spin behavior. In the ferromagnetic case, sites with fewer neighbors exhibit a higher tendency for spin flips at low temperatures, though this effect weakens as temperature increases, leading to a higher phase transition temperature than in the planar Ising model. In the antiferromagnetic case, lattice irregularities induce geometric frustration, resulting in highly degenerate ground states and the phase transition temperature lower than the planar square lattice. Phase transition temperatures are derived through specific heat, magnetic susceptibility analysis and GCNs predictions, yielding T c values for both ferromagnetic and antiferromagnetic scenarios. This work emphasizes the impact of the Fibonacci lattice’s geometric properties-namely curvature and connectivity-on spin interactions in non-planar systems, with relevance to microgravity environments.
Source: New Journal of Physics
Authors: Zheng Zhou, Chen-Hui Song, Xu-Yang Hou, Hao Guo
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
Awards: G4990087558, G6777568049
OpenAlex ID: W4416436698