%0 Journal Article %T Ground state of classical bilayer Wigner crystals %A L. Samaj %A E. Trizac %J Physics %D 2012 %I arXiv %R 10.1209/0295-5075/98/36004 %X 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. %U http://arxiv.org/abs/1205.2460v1