  Commonalities among the order parameters of the ubiquitous antiferromagnetism
present in the parent compounds of the iron arsenide high temperature
superconductors are explored. Additionally, comparison is made between the well
established two-dimensional Heisenberg-Ising magnet, K$_2$NiF$_4$ and iron
arsenide systems residing at a critical point whose structural and magnetic
phase transitions coincide. In particular, analysis is presented regarding two
distinct classes of phase transition behavior reflected in the development of
antiferromagnetic and structural order in the three main classes of iron
arsenide superconductors. Two distinct universality classes are mirrored in
their magnetic phase transitions which empirically are determined by the
proximity of the coupled structural and magnetic phase transitions in these
materials.
