Frustration in a spin model: chirality transitions via a variational analysis | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Frustration in a spin model: chirality transitions via a variational analysis

By Gianluca Orlando

Appears in collection : Beyond Elasticity: Advances and Research Challenges / Au-delà de l'élasticité : avancées dans la recherche et prochains défis

Spin models are lattice models that describe magnetic properties of materials. In this talk we will examine a 2-dimensional planar spin model (known as the J1-J2-J3 model) which exhibits frustration. Frustration is the phenomenon due to conflicting interatomic ferromagnetic/antiferromagnetic interactions that prevent the energy of every pair of interacting spins to be simultaneously minimized. The frustration mechanism leads to complex geometric patterns in the material. We study these complex geometric patterns by carrying out a discrete-to-continuum variational analysis as the lattice spacing tends to zero, finding the energetic regime for which many chiralphases can coexist. In particular, we will show that the surface tension between the chiral phases is captured by a continuum energy obtained by suitably selecting solutions to the eikonal equation. The results presented in the seminar are based on works in collaboration with M. Cicalese and M. Forster.

Information about the video

Date of recording 17/05/2022
Date of publication 17/06/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19918803
Cite this video Orlando, Gianluca (17/05/2022). Frustration in a spin model: chirality transitions via a variational analysis. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19918803
URL https://dx.doi.org/10.24350/CIRM.V.19918803

Domain(s)

Bibliography

CICALESE, Marco, FORSTER, Marwin, et ORLANDO, Gianluca. Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions. SIAM Journal on Mathematical Analysis, 2019, vol. 51, no 6, p. 4848-4893. - https://doi.org/10.1137/19M1257305
CICALESE, Marco, FORSTER, Marwin, et ORLANDO, Gianluca. Variational analysis of the $ J_1 $-$ J_2 $-$ J_3 $ model: a non-linear lattice version of the Aviles-Giga functional. arXiv preprint arXiv:2110.10047, 2021. - https://doi.org/10.48550/arXiv.2110.10047

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2024

Give feedback