Relaxation effects in the charge-ordered state of La$_{0.5}$Ca$_{0.5}$MnO$_{3}$

We report an experimental study of the time dependence of the resistivity and magnetization of charge-ordered La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ under different thermal and magnetic field conditions. A relaxation with a stretched exponential time dependence has been observed at temperatures below the charge ordering temperature. A model using a hierarchical distribution of relaxation times can explain the data.