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SUMMARY:A scaling law for a two-dimensional frustrated spin system
DTSTART:20230522T080000Z
DTEND:20230522T090000Z
DTSTAMP:20230924T174000Z
UID:indico-event-8273@indico.math.cnrs.fr
CONTACT:elise.bonhomme@universite-paris-saclay.fr
DESCRIPTION:Speakers: Melanie Koser (Humboldt-Universität zu Berlin)\n\nW
e are interested in pattern formation in two-dimensional magnetic compound
s. We consider materials whose atoms are ordered in a regular crystalline
structure and associate to each atom its so called spin\, a unit vector in
$\\mathbb{S}^1$. Complex geometric structures in the spin field may be th
e result of the competition between anti- and ferromagnetic interactions.
In ferromagnetic materials spins prefer to be aligned\, whereas in antifer
romagnetic compounds one cannot observe a global orientation of the spins.
The competition between these two interactions leads to frustration mecha
nisms in the system. We consider the lattice energy of certain materials\,
in which antiferromagnetic (AF) and ferromagnetic (F) interactions coexis
t\, and are modeled by the $J_1 $-$J_3$ F-AF model on a square lattice. In
this talk we present our current research results. These include a scalin
g law for the optimal energy\, which also describes arising patterns in a
minimal spin field. Further\, we discuss a $\\Gamma$-convergence result wh
ich in a certain parameter regime relates the discrete model with a suitab
le continuous counterpart.Based on a joint work with Janusz Ginster and Ba
rbara Zwicknagl.\n\nhttps://indico.math.cnrs.fr/event/8273/
URL:https://indico.math.cnrs.fr/event/8273/
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