Bound state attraction threshold in the layered Hubbard model

The condition of the existence of a bound 2-particle state (BS) is examined in the empty lattice limit within the attractive Hubbard model on layered systems. It is known, that in low-dimensional systems an infinitesimal attraction suffices to form BS, while in three dimensions (3d), a threshold must be reached. Current results indicate an abrupt transition between "infinitesimal" and "finite threshold" regimes with an increasing number of layers for infinite systems and smooth crossover for finite ones.