# On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials

@inproceedings{Luo2021OnUO, title={On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials}, author={Senping Luo and Juncheng Wei and Wenming Zou}, year={2021} }

We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely monotone functions among lattices is located exactly on a special curve which is part of the boundary of the fundamental region. We also establish a universal result for square lattice being the optimal in certain interval, which is surprising. Our result establishes the hexagonal-rhombic-square…

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