We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) nonperiodic lattice close to a flat set in a lower-dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter ε > 0, we perform a 0-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue of stochastic homogenization in the case of random stationary lattices. A finer dependence of the homogenized energy on the average thickness of the random lattice is analyzed for an example of a magnetic thin system obtained by a random deposition mechanism.
Braides, A., Cicalese, M., Ruf, M. (2018). Continuum limit and stochastic homogenization of discrete ferromagnetic thin films. ANALYSIS & PDE, 11(2), 499-553 [10.2140/apde.2018.11.499].
Continuum limit and stochastic homogenization of discrete ferromagnetic thin films
Braides, Andrea;
2018-01-01
Abstract
We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) nonperiodic lattice close to a flat set in a lower-dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter ε > 0, we perform a 0-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue of stochastic homogenization in the case of random stationary lattices. A finer dependence of the homogenized energy on the average thickness of the random lattice is analyzed for an example of a magnetic thin system obtained by a random deposition mechanism.File | Dimensione | Formato | |
---|---|---|---|
BCR_final.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Copyright dell'editore
Dimensione
592.3 kB
Formato
Adobe PDF
|
592.3 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.