  We study a lattice model for Marginal Fermi liquid behavior, involving a gas
of electrons coupled to a dense lattice of three-body bound-states. The
bound-states change the phase space for electron-electron scattering and induce
a marginal self-energy amongst the electron gas. When the three-body
bound-states are weakly coupled to the electron gas, there is a substantial
window for marginal Fermi liquid behavior. In this regime, the model displays
the presence of two relaxation times, one linear, one quadratic in the
temperature. At low temperatures the bound-states develop coherence leading to
a cross-over to conventional Fermi liquid behavior. At strong-coupling,
marginal Fermi liquid behavior is pre-empted by a pairing or magnetic
instability, and it is not possible to produce a linear scattering rate
comparable with the temperature. We discuss the low temperature instabilities
of this model and compare it to the Hubbard model at half-filling.
