Variational analysis of a two-dimensional frustrated spin system: Emergence and rigidity of chirality transitions

We study the discrete-to-continuum variational limit of the J₁-J₃ spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. Carrying out the Γ-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.