# American Institute of Mathematical Sciences

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

 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.
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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