  The spin-spin correlation length and the static structure factor for bilayer
antiferromagnets, such as YBa$_2$Cu$_3$O$_{6}$, are calculated using field
theoretical and numerical methods. It is shown that these quantities can be
directly measured in neutron scattering experiments using energy integrated
two-axis scan despite the strong intensity modulation perpendicular to the
layers. Our calculations show that the correlation length of the bilayer
antiferromagnet diverges considerably more rapidly, as the temperature tends to
zero, than the correlation length of the corresponding single layer
antiferromagnet typified by La$_2$CuO$_4$. This rapid divergence may have
important consequences with respect to magnetic fluctuations of the doped
superconductors.
