Random one-body approximation to the Hubbard model. III. Application to higher-dimensional lattices

Abstract

In this, the last of a sequence of papers dealing with a new random one-body approximation to the Hubbard Hamiltonian, we examine higher-dimensional systems. Thermodynamics and transport properties (dc conductivity) of the model are calculated using our self-consistent approach. A magnetic phase transition is found to occur at a critical temperature ${T}_{c}$, which seems to be second order when the ratio $\frac{U}{B}$ of the electron-electron repulsion $U$ to the unperturbed half-bandwidth $B$ exceeds a critical value and first order otherwise. At low temperatures the system is found to be an insulator with nonzero local moment while for high temperatures and low $\frac{U}{B}$, it is a normal metal with zero local moment. The dc conductivity that we obtain from the present model exhibits a behavior characteristic of certain transition-metal compounds.