  We construct an effective spin model from the coupled spin-fermion problem
appropriate to double perovskites of the form A_2BB'O_6. The magnetic model
that emerges is reminiscent of double exchange and we illustrate this
`reduction' in detail for the case of perfect B-B' structural order, i.e, no
antisite disorder. We estimate the effective exchange between the magnetic B
ions in terms of the electronic parameters, study the `classical' magnetic
model using Monte Carlo techniques, and compare this approach to a full
numerical solution of the spin-fermion problem. The agreement is reasonable,
and promises a quick estimate of magnetic properties when coupled with ab
initio electronic structure. The scheme generalises to the presence of antisite
disorder.
