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

Abstract

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.

arXiv comment53 pages, 3 figures

References in corpus (12)

• Topological domain walls in helimagnets
• Checkerboards, stripes and corner energies in spin models with competing interactions
• Interfaces, modulated phases and textures in lattice systems
• Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
• Periodic striped ground states in Ising models with competing interactions
• Formation of stripes and slabs near the ferromagnetic transition
• Characterization of minimizers of Aviles-Giga functionals in special domains
• Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture
• A regularizing property of the $2D$-eikonal equation
• The $N$-clock model: Variational analysis for fast and slow divergence rates of $N$
• The rectifiability of the entropy defect measure for Burgers equation
• On the structure of weak solutions to scalar conservation laws with finite entropy production