For α ≥ 3/2, the lattice energy Σ |P|^4 e^{-πα|P|^2} over unit-density 2D lattices is uniquely minimized by the hexagonal lattice.
B´ etermin, Two-dimensional theta functions and crystallization among Bravais lattices, SIAM Journal on Mathematical Analysis, 48(5) (2016), 3236-269
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Minimizing Lattice Energy and Hexagonal Crystallization
For α ≥ 3/2, the lattice energy Σ |P|^4 e^{-πα|P|^2} over unit-density 2D lattices is uniquely minimized by the hexagonal lattice.