# Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions

created by orlando on 17 Apr 2019
modified by cicalese on 02 Sep 2019

[BibTeX]

Accepted Paper

Inserted: 17 apr 2019
Last Updated: 2 sep 2019

Journal: SIAM J. Math. Anal.
Year: 2019

ArXiv: 1904.07792 PDF

Abstract:

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.