Numerical simulations: some results for the 2- and 3-D Hubbard models and a 2-D electron phonon model

Numerical simulations on the half-filled 3-D Hubbard model clearly show the onset of Néel order. Simulations of the 2-D electron-phonon Holstein model show the competition between the formation of a Peierls-CDW state and a superconducting state. However, the behavior of the partly filled 2-D Hubbard model is more difficult to determine. At half-filling, the anti-ferromagnetic correlations grow as T is reduced. Doping away from half-filling supresses these correlations, and we find that there is a weak attractive pairing interaction in the d -wave channel. However, the strength of the pair field susceptibility is weak at the temperatures and lattice sizes we have simulated, and the nature of the low-temperature state of the nearly half-filled Hubbard model remains open.