Exploring the Energy Landscape of the Logarithmic Potential: Local Minima and Stationary States

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 \(N_\textrm{conf}\) (number of distinct configurations) is exponential, as for the Thomson problem, although weaker. Using the techniques described in our previous paper [1] we have also explored the solution landscape of this problem for \(N \le 24\), and found that the number of stationary states is growing exponentially.