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We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$spin model on the square lattice in the vicinity of the helimagnet/ferromagnettransition point as the lattice spacing vanishes. Carrying out the$\Gamma$-convergence analysis of proper scalings of the energy, we prove theemergence and characterize the geometric rigidity of the chirality phasetransitions.

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