Calculus of Variations and Geometric Measure Theory

A. Braides

Rigidity effects for antiferromagnetic thin films: a prototypical example

created by braidesa on 31 Mar 2017
modified on 30 Apr 2018


Book Chapter- Trends in Applications of Mathematics to Mechanics (E.Rocca et al, eds) Springer

Inserted: 31 mar 2017
Last Updated: 30 apr 2018

Year: 2018
Doi: 10.1007/978-3-319-75940-1_10


We consider two-dimensional discrete thin films obtained from $N$ layers of a triangular lattice, governed by an antiferromagnetic energy. By a dimension-reduction analysis we show that, in contrast with the ``total frustration'' of the triangular lattice, the overall behaviour of the thin film is described by a limit interfacial energy on functions taking $2^N$ distinct parameters. In a sense, then the total frustration is recovered as $N$ tends to infinity.