  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/ferromagnet
transition point as the lattice spacing vanishes. Carrying out the
$\Gamma$-convergence analysis of proper scalings of the energy, we prove the
emergence and characterize the geometric rigidity of the chirality phase
transitions.
