Low temperature broken symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of large spin S, there is a zero temperature (T) Lifshitz point at J3 = (1/4) J1, with long-range spiral spin order at T=0 for J3 > (1/4) J1. We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0 <= T < Tc ~ (J3-(1/4) J1) S^2. The transition at T=Tc is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.