American Institute of Mathematical Sciences

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March  2006, 1(1): 85-107. doi: 10.3934/nhm.2006.1.85

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

Roberto Alicandro 1, , Andrea Braides 2, and  Marco Cicalese 3,

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, Italy

Received  September 2005 Revised  October 2005 Published  January 2006

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.
Keywords: surface energies, binary alloys., anti-phase boundaries, $\Gamma$-convergence, spin systems, Lattice systems.
Mathematics Subject Classification: Primary: 49S05, 49J45, 82B20, 82B24; Secondary: 49M25, 49Q20, 49Q2.
Citation: Roberto Alicandro, Andrea Braides, Marco Cicalese. Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint. Networks & Heterogeneous Media, 2006, 1 (1) : 85-107. doi: 10.3934/nhm.2006.1.85
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