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arXiv · 2506.08398

Exploring the energy landscape of the Thomson problem: local minima and stationary states

Paolo Amore·Victor Figueroa·Enrique Diaz·Jorge A. López·Trevor Vincent
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Abstract

We conducted a comprehensive numerical investigation of the energy landscape of the Thomson problem for systems up to $N=150$. Our results show the number of distinct configurations grows exponentially with $N$, but significantly faster than previously reported. Furthermore, we find that the average energy gap between independent configurations at a given $N$ decays exponentially with $N$, dramatically increasing the computational complexity for larger systems. Finally, we developed a novel approach that reformulates the search for stationary points in the Thomson problem (or similar systems) as an equivalent minimization problem using a specifically designed potential. Leveraging this method, we performed a detailed exploration of the solution landscape for $N\leq24$ and estimated the growth of the number of stationary states to be exponential in $N$.

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Paolo Amore, Victor Figueroa, Enrique Diaz, Jorge A. López, Trevor Vincent. 2025-06-10. Exploring the energy landscape of the Thomson problem: local minima and stationary states. https://arxiv.org/abs/2506.08398

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