Chirality transitions in frustrated S2-valued spin systems

We study the discrete-to-continuum limit of the helical XY [Formula: see text]-spin system on the lattice [Formula: see text]. We scale the interaction parameters in order to reduce the model to a spin chain in the vicinity of the Landau–Lifschitz point and we prove that at the same energy scaling under which the [Formula: see text]-model presents scalar chirality transitions, the cost of every vectorial chirality transition is zero. In addition we show that if the energy of the system is modified penalizing the distance of the [Formula: see text]-field from a finite number of copies of [Formula: see text], it is still possible to prove the emergence of nontrivial (possibly trace-dependent) chirality transitions.