Calculus of Variations and Geometric Measure Theory

M. Cicalese - M. Forster - G. Orlando

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 Apr 2021


Published Paper

Inserted: 17 apr 2019
Last Updated: 2 apr 2021

Journal: SIAM J. Math. Anal.
Volume: 51
Number: 2
Pages: 4848-4893
Year: 2019

ArXiv: 1904.07792 PDF


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.