2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57577We study the `asymmetric' Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov-Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.12 pagesMathematical PhysicsStatistical MechanicsStrongly Correlated Electrons82B10, 82B20, 82B26text