Monte Carlo Study of the Two-Dimensional Hubbard Model

A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6×6 spatial sites, as a function of temperature and electron-electron repulsion $U$. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of $U$, although greatly reduced from the mean-field-theory predictions.