  We use a Green's function method to study the temperature-dependent average
moment and magnetic phase-transition temperature of the striped
antiferromagnetism of LaFeAsO, and other similar compounds, as the parents of
FeAs-based superconductors. We consider the nearest and the next-nearest
couplings in the FeAs layer, and the nearest coupling for inter-layer spin
interaction. The dependence of the transition temperature TN and the
zero-temperature average spin on the interaction constants is investigated. We
obtain an analytical expression for TN and determine our temperature-dependent
average spin from zero temperature to TN in terms of unified self-consistent
equations. For LaFeAsO, we obtain a reasonable estimation of the coupling
interactions with the experimental transition temperature TN = 138 K. Our
results also show that a non-zero antiferromagnetic (AFM) inter-layer coupling
is essential for the existence of a non-zero TN, and the many-body AFM
fluctuations reduce substantially the low-temperature magnetic moment per Fe
towards the experimental value. Our Green's function approach can be used for
other FeAs-based parent compounds and these results should be useful to
understand the physical properties of FeAs-based superconductors.
