Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint

2006, Volume 1, Issue 1: 85-107. doi: 10.3934/nhm.2006.1.85

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1.
DAEIMI, Università di Cassino, via Di Biasio, 03043 Cassino (FR)
2.
Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma
3.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli

We provide a variational description of nearest-neighbours and next-to-nearest neighbours binary lattice systems. By studying the $\Gamma$-limit of proper scaling of the energies of the systems, we highlight phase and anti-phase boundary phenomena and show how they depend on the geometry of the lattice.
- Lattice systems,
- $\Gamma$-convergence,
- anti-phase boundaries,
- surface energies,
- spin systems,
- binary alloys
Citation: Roberto Alicandro, Andrea Braides, Marco Cicalese. Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint[J]. Networks and Heterogeneous Media, 2006, 1(1): 85-107. doi: 10.3934/nhm.2006.1.85

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Abstract

We provide a variational description of nearest-neighbours and next-to-nearest neighbours binary lattice systems. By studying the $\Gamma$-limit of proper scaling of the energies of the systems, we highlight phase and anti-phase boundary phenomena and show how they depend on the geometry of the lattice.
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© 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)