Exploring the energy landscape of the logarithmic potential: local minima and stationary states
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| Format: | Preprint |
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2025
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| _version_ | 1866911316794408960 |
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| author | Amore, Paolo Figueroa, Victor Ramos, Raymundo |
| author_facet | Amore, Paolo Figueroa, Victor Ramos, Raymundo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring the energy landscape of the logarithmic potential: local minima and stationary states Amore, Paolo Figueroa, Victor Ramos, Raymundo Soft Condensed Matter Computational Physics 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. |
| title | Exploring the energy landscape of the logarithmic potential: local minima and stationary states |
| topic | Soft Condensed Matter Computational Physics |
| url | https://arxiv.org/abs/2512.12416 |