Antiferromagnetism in the Two-Dimensional Hubbard Model

Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8×8 and temperatures down to $T=\frac{t}{20}$ ($t=\mathrm{hopping}$) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion $U$. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.