  We study the effect of quenched disorder on the ordering of orbital and
magnetic degrees of freedom in a two-dimensional, two-band double-exchange
model for $e_g$ electrons coupled to Jahn-Teller distortions. Using a
real-space Monte Carlo method, we find that disorder can induce a short-range
ordering of the orbital degrees of freedom near 30% hole doping. The most
striking consequence of this short range ordering is a strong increase in the
low temperature resistivity. The real-space approach allows to analyze the
spatial patterns of the charge, orbital, and magnetic degrees of freedom, and
the correlations among them. The magnetism is inhomogeneous on the nanoscale in
the short-range orbitally ordered state.
