  We study a number of different ingredients, related to long range order
observed in lattice QCD simulations, using a simple "deformed QCD" model. This
model is a weakly coupled gauge theory, which however has all the relevant
crucial elements allowing us to study difficult and nontrivial problems which
are known to be present in real strongly coupled QCD. In the present study, we
want to understand the physics of long range order in form of coherent low
dimensional vacuum configurations observed in Monte Carlo lattice simulations.
We demonstrate the presence of double-layer domain wall structures in the
deformed QCD, and study their interaction with localized topological monopoles.
Furthermore, we show that there is in fact an attractive interaction between
the two, such that the monopole favors a position within the domain wall.
