Frustrated ferromagnetic spin chains: a variational approach to chirality transitions

We study the energy per particle of a one-dimensional ferromagnetic/anti-ferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close to the helimagnet/ferromagnet transition point as the number of particles diverges. We rigorously prove the emergence of chiral ground states and we compute, by performing the Gamma-limits of proper renormalizations and scalings, the energy for a chirality transition.