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arXiv · 2512.12416

Exploring the energy landscape of the logarithmic potential: local minima and stationary states

Paolo Amore·Victor Figueroa·Raymundo Ramos
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Abstract

We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of $N_{\rm conf}$ (number of distinct configurations) is exponential, as for the Thomson problem, although weaker. Using the techniques described in our previous paper~\cite{Amore25} we have also explored the solution landscape of this problem for $N \leq 24$, and found that the number of stationary states is growing exponentially.

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Paolo Amore, Victor Figueroa, Raymundo Ramos. 2025-12-13. Exploring the energy landscape of the logarithmic potential: local minima and stationary states. https://arxiv.org/abs/2512.12416

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