For odd dimensions with interaction powers (a,b)=(3,2-d) and even dimensions with (3,1-d), the unique energy minimizer is given explicitly, with d=1,2,3 in elementary functions.
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A family of explicit minimizers for interaction energies
For odd dimensions with interaction powers (a,b)=(3,2-d) and even dimensions with (3,1-d), the unique energy minimizer is given explicitly, with d=1,2,3 in elementary functions.