Mott-Hubbard transition in infinite dimensions

We analyze the unanalytical structure of metal-insulator transition (MIT) in infinite dimensions. A multiple-valued structure in Green's function and other thermodynamical quantities with respect to the interaction strength U are observed at low temperatures by introducing a transformation into the dynamical mean-field equation of Hubbard model. A complete description of stable, metastable, and unstable phases is established in the regime U-c1(T) < U < U-c2(T). The Maxwell construction is performed to evaluate the MIT line U*(T). We show how the first-order MIT at U* (T) for T>0 evolves into the second-order one at U-c2(0) for T=0. The phase diagram near MIT is presented.