  An analysis of the properties of half-doped manganites is presented. We build
up the phase diagram of the system combining a realistic calculation of the
electronic properties and a mean field treatment of the temperature effects.
The electronic structure of the manganites are described with a double exchange
model with cooperative Jahn-Teller phonons and antiferromagnetic coupling
between the $Mn$ core spins. At zero temperature a variety of electronic phases
as ferromagnetic (FM) charge ordered (CO) orbital ordered (OO), CE-CO-OO and FM
metallic, are obtained. By raising the temperature the CE-CO-OO phase becomes
paramagnetic (PM), but depending on the electron-phonon coupling and the
exchange coupling the transition can be direct or trough intermediate states: a
FM disorder metallic, a PM-CO-OO or a FM-CO-OO. We also discus the nature of
the high temperature PM phase in the regime of finite electron phonon coupling.
In this regime half of the oxygen octahedra surrounding the $Mn$ ions are
distorted. In the weak coupling regime the octahedra are slightly deformed and
only trap a small amount of electronic charge, rendering the system metallic
consequentially. However in the strong coupling regime the octahedra are
strongly distorted, the charge is fully localized in polarons and the system is
insulator.
