Calculus of Variations and Geometric Measure Theory

M. Cicalese - M. Forster - G. Orlando

Variational analysis of the $J_1$-$J_2$-$J_3$ model: a non-linear lattice version of the Aviles-Giga functional

created by orlando on 29 Aug 2021
modified by cicalese on 17 Sep 2023


Published Paper

Inserted: 29 aug 2021
Last Updated: 17 sep 2023

Journal: Arch. Ration. Mech. anal.
Volume: 245
Number: 2
Pages: 1135–1196
Year: 2022


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.

Keywords: Gamma-convergence, Eikonal equation, Chirality transitions, frustrated spin systems, Aviles-Giga functional