Low-temperature broken-symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J(1)) and third- (J(3)) neighbor exchange on the square lattice. In the limit of spin S --> infinity, there is a zero temperature ( T) Lifshitz point at J(3) = 1/4 J(1), with long-range spiral spin order at T = 0 for J(3) > 1/4 J(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 less than or equal to T < T-c ∼ (J(3) - 1/4 J(1)) S-2. The transition at T = T-c is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.