On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials
Abstract
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 hexagonalrhombicsquarerectangular transition lattice shapes in many physical and biological system (such as BoseEinstein condensates and twocomponent GinzburgLandau systems). It turns out, our results also apply to locating the minimizers of sum of two Eisenstein series, which is new in number theory.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08728
 Bibcode:
 2021arXiv211008728L
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematical Physics
 EPrint:
 32 pages