@article{Kubin2023, 
author = {Andrea Kubin and Lorenzo Lamberti},
title = {Variational analysis in one and two dimensions of a frustrated spin system: chirality and magnetic anisotropy transitions},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {6},
pages = {1-37},
keywords = {Γ-convergence, frustrated lattice systems, chirality transitions},
url = {https://www.sciopen.com/article/10.3934/mine.2023094},
doi = {10.3934/mine.2023094},
abstract = {We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system where the spin takes values on two disjoint circles of the 2-dimensional unit sphere. This analysis will be carried out first on a one-dimensional lattice and then on a two-dimensional lattice. The energy consists of the sum of a term that depends on nearest and next-to-nearest interactions and a penalizing term related to the spins' magnetic anisotropy transitions. We analyze the asymptotic behaviour of the energy, that is when the system is close to the helimagnet/ferromagnet transition point as the number of particles diverges. In the one-dimensional setting we compute the    Γ-limit of scalings of the energy at first and second order. As a result, it is shown how much energy the system spends for any magnetic anistropy transition and chirality transition. In the two-dimensional setting, by computing the    Γ-limit of a scaling of the energy, we study the geometric rigidity of chirality transitions.}
}