  Within the Green's function and equations of motion formalism it is possible
to exactly solve a large class of models useful for the study of strongly
correlated systems. Here, we present the exact solution of the one-dimensional
extended Hubbard model with on-site $U$ and first nearest neighbor repulsive V
interactions in the presence of an external magnetic field h, in the narrow
band limit. At zero temperature our results establish the existence of four
phases in the three-dimensional space (U, n, h) - n is the filling - with
relative phase transitions, as well as different types of charge ordering. The
magnetic field may dramatically affect the behavior of thermodynamic
quantities, inducing, for instance, magnetization plateaus in the magnetization
curves, and a change from a single to a double-peak structure in the specific
heat. According to the value of the particle density, we find one or two
critical fields, marking the beginning of full or partial polarization. A
detailed study of several thermodynamic quantities is also presented at finite
temperature.
