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 spin S-->infinity, there is a zero temperature (T) Lifshitz point at J(3)=1/4J(1), with long-range spiral spin order at T=0 for J3>1/4J(1). 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< or =T<T(c) approximately (J3-1/4J(1))S2. The transition at T=T(c) is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.