Global Minimality of triangular lattice among Bravais lattices

2D Theta Functions and Crystallization among Bravais Lattices

Minimization problems among bravais lattices for finite energy per point are studied for some general potentials.We prove that if a function is completely monotonic, then the triangular lattice minimizes energy per particle among bravaislattices with density fixed for any density.Furthermore we give an example of convex decreasing positive potential for which triangular lattice is not aminimizer for some densities.Finally we deduce global minimality among all bravais lattices, i.e.Without density constraint, of a triangular lattice for some parameters of lennard-jones type potentials and attractive-repulsive yukawa potentials.