  We show that the magnetism of double perovskite AFe_{1/2}M_{1/2}O_3 systems
may be described by the Heisenberg model on the simple cubic lattice, where
only half of sites are occupied by localized magnetic moments. The
nearest-neighbor interaction J_1 is more than 20 times the next-nearest
neighbor interaction J_2, the third-nearest interaction along the space
diagonal of the cube being negligible. We argue that the variety of magnetic
properties observed in different systems is connected with the variety of
chemical ordering in them. We analyze six possible types of the chemical
ordering in 2x2x2 supercell, and argue that the probability to find them in a
real compound does not correspond to a random occupation of lattice sites by
magnetic ions. The exchange J_2 rather than J_1 define the magnetic energy
scale of most double perovskite compounds that means the enhanced probability
of 1:1 short range ordering. Two multiferroic compounds PbFe_{1/2}M_{1/2}O_3
(M=Nb, Ta) are exceptions. We show that the relatively high temperature of
antiferromagnetic transition is compatible with a layered short-range chemical
order, which was recently shown to be most stable for these two compounds [I.
P. Raevski, {\em et al.}, Phys.\ Rev.\ B \textbf{85}, 224412 (2012)]. We show
also that one of the types of ordering has ferrimagnetic ground state. The
clusters with short-range order of this type may be responsible for a
room-temperature superparamagnetism, and may form the cluster glass at low
temperatures.
