Finite-Temperature Phase Diagram of the Hubbard Model

The finite-temperature phase diagram of the Hubbard model in $d=3$ is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%--40% electron or hole doping from half filling, a new $\tau$ phase in which the electron hopping strength $t$ asymptotically becomes infinite under repeated rescalings. Next to the $\tau$ phase, a first-order phase boundary with very narrow phase separation (less than 2% jump in electron density) occurs. At temperatures above the $\tau$ phase, an incommensurate spin modulation phase is indicated. In $d=2$, we find that the Hubbard model has no phase transition at finite temperature.