The Phase Transition in 5 Point Energy Minimization

Richard Evan Schwartz

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arXiv · 1610.03303

The Phase Transition in 5 Point Energy Minimization

Richard Evan Schwartz

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Abstract

Let R_s(r)=sign(s)/r^s be the Riesz s-energy potential. (This is the usual power-law potential.) This monograph proves the existence of a computable number S=15.048... such that the triangular bi-pyramid is the unique minimizer with respect to R_s, amongst all 5-point configurations on the sphere, if and only if s lies in (-2,0) or (0,S). This establishes the existence of the long-conjectured phase transition constant in 5-point energy minimization.

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BibTeX RIS

Richard Evan Schwartz. 2016-10-11. The Phase Transition in 5 Point Energy Minimization. https://arxiv.org/abs/1610.03303

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