We present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic ${4}^{3}$ lattices and some ${6}^{3}$ 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 present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic ${4}^{3}$ lattices and some ${6}^{3}$ 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.

Physical review. B, Condensed matterFeb 1, 198793 citations

t-J model at 50

Józef Spałek

I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three--orbital situation. The main purpose is to list some basic features of the physics associated with t--J model.I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three--orbital situation. The main purpose is to list some basic features of the physics associated with t--J model.

arXiv:2609.35178Sep 28, 20260 citations

We present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic

{4}^{3}

lattices and some

{6}^{3}

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.