  Motivated by recent neutron scattering experiments, we study the ordering of
spins in the iron-based superconductors La(O_{1-x}F_x)FeAs, assuming them in
proximity to a Mott insulator in the phase diagram. The ground state of the
parent system with x = 0 is a spin density wave with ordering wave vector Q =
(0, \pi) or (\pi, 0). Upon raising the temperature, we find the system to
restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the
experimentally observed lattice distortion to a monoclinic crystal structure.
Upon further temperature increase, the spins finally disorder at a second
transition. The phase transition driven by doping with charge carriers
similarly splits into an O(3) transition, and an Ising transition with z = 3 at
larger doping.
