Calculus of Variations and Geometric Measure Theory

A. Braides - M. Cicalese - N. K. Yip

Crystalline Motion of Interfaces Between Patterns

created by cicalese on 20 Apr 2016
modified by braidesa on 09 Oct 2016


Published Paper

Inserted: 20 apr 2016
Last Updated: 9 oct 2016

Journal: J. Stat. Phys.
Volume: 165
Number: 2
Pages: 274-319
Year: 2016
Doi: 10.1007/s10955-016-1609-6


We consider the dynamical problem of an antiferromagnetic spin system on a twodimensional square lattice $\varepsilon{\mathbb Z}^2$ with nearest-neighbour and next-to-nearest neighbour interactions. The key features of the model include the interaction between spatial scale $\varepsilon$ and time scale $\tau$, and the incorporation of interfacial boundaries separating regions with microstructures. By employing a discrete-time variational scheme, a limit continuous-time evolution is obtained for a crystal in ${\mathbb R}^2$ which evolves according to some motion by crystalline curvatures. In the case of anti-phase boundaries between striped patterns, a striking phenomenon is the appearance of some ``non-local'' curvature dependence velocity law reflecting the creation of some defect structure on the interface at the discrete level.