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Modelling itinerant ferromagnetism still poses major challenges to theoreticians. In 1963 John Hubbard proposed [1] a single-band model, but, as it turned out, ferromagnetism only appears within mean-field approximations. Since then, distinct routes to ferromagnetism have been proposed, some of which are based on multi-band models. The development of this route was boosted by a theorem proved by Elliott Lieb [2], according to which the Hubbard model on bipartite lattices with unequal number of sites on each sublattice, and at half filling, should have a non-zero spin in the ground state. While a total non-zero spin is suggestive of long-range order (LRO), a systematic investigation of LRO had not been carried out so far. Another issue of interest is whether Lieb’s theorem can be extended to lattices in which the on-site repulsion is inhomogeneous. An example of a lattice falling under the conditions of the theorem is the ‘CuO2 lattice (also known as ‘Lieb lattice’, or as a decorated square lattice), in which ‘d-orbitals’ occupy the vertices of the squares, while ‘p-orbitals’ lie halfway between two d-orbitals; both d and p orbitals can accommodate only up to two electrons. In this talk we report on Determinant Quantum Monte Carlo (DQMC) simulations for the Lieb lattice [3]. We quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud = Up, originally considered by Lieb, and the inhomogeneous (IH) case, Ud ̸= Up. For the H case at half filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the