  We study the occurrence of symmetry breakings, at zero and finite
temperatures, in the J_1-J_3 antiferromagnetic Heisenberg model on the square
lattice using Schwinger boson mean field theory. For spin-1/2 the ground state
breaks always the SU(2) symmetry with a continuous quasi-critical transition at
J_3/J_1=0.38, from N\'eel to spiral long range order, although local spin
fluctuations considerations suggest an intermediate disordered regime around
0.35 < J_3/J_1 < 0.5, in qualitative agreement with recent numerical results.
At low temperatures we find a Z_2 broken symmetry region with short range
spiral order characterized by an Ising-like nematic order parameter that
compares qualitatively well with classical Monte Carlo results. At intermediate
temperatures the phase diagram shows regions with collinear short range orders:
for J_3/J_1<1 N\'eel (\pi,\pi) correlations and for J_3/J_1>1 a novel phase
consisting of four decoupled third neighbour sublattices with N\'eel (\pi,\pi)
correlations in each one. We conclude that the effect of quantum and thermal
fluctuations is to favour collinear correlations even in the strongly
frustrated regime.
