  Recent experiments in Pr(Nd)$_{0.5}$Ca$_{0.5}$MnO$_3$ thin films exhibited
(multiple) reentrant charge ordering (CO) transitions with change of {\it
temperature} T under fixed magnetic field H, which are in contrast to the
results for the corresponding bulk materials. To explain the experimental
findings, a model including the double-exchange mechanism, intersite Coulomb
interaction and electron-phonon coupling is proposed, for which the reentrant
CO is naturally obtained due to the temperature dependence of the band-type
coherent polaron hopping. Various results for the CO in the (H, T) plane are
extensively discussed. The theory is considered to be valid for both thin films
and bulk materials.
