Using the cluster Bethe lattice method and the quasi-spin model for itinerant magnetism, the authors show that in a one-band model there is no metallic-antiferromagnetic phase for a half-filled band at T=0.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
We present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic 43 lattices and some 63 lattices with periodic boundary conditions, as well as of small clusters embedded in an effective medium. Magnetic properties were studied for values of the Hubbard repulsion U ranging from 0 to the bandwidth W=12t (t is the hopping matrix element). Our results show that antiferromagnetism is enhanced up to U\ensuremath{\sim}(5/6)W and then suppressed. The q=0 magnetic susceptibility is enhanced by U, although much less than predicted by the random-phase approximation. The transition temperature to an antiferromagnetic state is found to have a broad maximum around U\ensuremath{\sim}(5/6)W, with a maximum value of approximately W/18. The implications of our results for superconductivity in the attractive Hubbard model are also discussed.
We study the Hubbard model on the triangular lattice for general fillings by means of the slave-boson technique. In particular, we consider the stability regions of the paramagnetic, antiferromagnetic and linearly polarized spin-density-wave phases that are present at half-filling. The model presents a large anisotropy under particle or hole doping of the half-filled band, a consequence of the non-bipartite nature of the lattice. We also compute the helicity modulus in the antiferromagnetic phase, which characterizes the stiffness of the magnetic order.