Variational Analysis of the $$J_1$$–$$J_2$$–$$J_3$$ Model: A Non-linear Lattice Version of the Aviles–Giga Functional

Abstract

AbstractWe study the variational limit of the frustrated $$J_1$$ J 1 –$$J_2$$ J 2 –$$J_3$$ 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 $$\Gamma $$ Γ -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.