  The large $J_2$ limit of the square-lattice $J_1-J_2$ Heisenberg
antiferromagnet is a classic example of order by disorder where quantum
fluctuations select a collinear ground state. Here, we use series expansion
methods and a meanfield spin-wave theory to study the excitation spectra in
this phase and look for a finite temperature Ising-like transition,
corresponding to a broken symmetry of the square-lattice, as first proposed by
Chandra et al. (Phys. Rev. Lett. 64, 88 (1990)). We find that the spectra
reveal the symmetries of the ordered phase. However, we do not find any
evidence for a finite temperature phase transition. Based on an effective field
theory we argue that the Ising-like transition occurs only at zero temperature.
