2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102006We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model. The critical line is established to lowest order in the tunneling amplitude.20 pagesMathematical PhysicsStatistical Mechanics82B10, 82B20, 82B26text