  We study the variational limit of the frustrated $J_1$-$J_2$-$J_3$ spin model
on the square lattice in the vicinity of the ferromagnet/helimagnet transition
point as the lattice spacing vanishes. We carry out the $\Gamma$-convergence
analysis of proper scalings of the energy and we characterize the optimal cost
of a chirality transition in $BV$ proving that the system is asymptotically
driven by a discrete version of a non-linear perturbation of the Aviles-Giga
energy functional.
