We discuss the Mott-Hubbard transition in light of the Hubbard model in infinite dimensions with special emphasis on the finite-temperature aspects of the problem. We demonstrate that the Mott transition at finite temperatures has a first-order character. We determine the region where metallic and insulating solutions coexist using second-order perturbation theory and we draw the phase diagram of the Hubbard model at half filling with a semicircular density of states. We discuss the lessons learned from the present treatment of the Hubbard model and the connection to other approximation schemes and to experiments on transition-metal oxides.

• Received 1 October 1993

DOI:https://doi.org/10.1103/PhysRevB.49.10181