Ground state of classical bilayer Wigner crystals

We study the ground-state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario —including critical phenomena— can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hitherto plagued by the inaccuracies inherent to long-range interaction potentials.