Two-particle correlations in finite low-dimensional Hubbard-like lattices

The ground-state properties of two particles (or two holes) with different masses in finite low-dimensional lattices with periodic boundary conditions is investigated rigorously in a Hubbard-like model with external field. A sufficient strong field results in ferromagnetic ordering, and we found the conditions, when the creation of two holes near half-filling for hypercubes in d=1, 2, 3 dimensions with even numbers of atoms (for bipartite lattices) and with odd numbers of atoms (for non-bipartite lattices), leads to instability of the ferromagnetic Nagaoka state against spin-flip in the strong interaction limit. The criteria for ferromagnetic stability in lattices consisting of different numbers (odd or even) of particles and lattice sites are also found and represent a qualitative explanation of the strong spontaneous ferromagnetism sometimes seen in small clusters of atoms, such as in rhodium. ((orig.))