On the optimality of the rock-salt structure among lattices with charge distributions

The goal of this paper is to investigate the optimality [Formula: see text]-dimensional rock-salt structure, i.e. cubic lattice text] volume with an alternation charges at points, among periodic distributions and structures. We assume that are interacting through two types radially symmetric interaction potentials, according their signs. first restrict our study class orthorhombic lattices. prove that, for energy model, structure always a critical point structures fixed density. This holds large potentials. then minimization problem lattices inverse power laws Gaussian High density minimality results low-density non-optimality derived both Numerically, we several particular cases in dimensions text], text]. numerics support conjecture global optimum all charges, satisfying some natural constraints. For observe phase transition type “triangular-rhombic-square-rectangular” minimizer’s shape as decreases.