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

Pages: 85 - 107, Volume 1, Issue 1, March 2006

doi:10.3934/nhm.2006.1.85       Abstract        Full Text (285.9K)       Related Articles

Roberto Alicandro - DAEIMI, Università di Cassino, via Di Biasio, 03043 Cassino (FR), Italy (email)
Andrea Braides - Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma, Italy (email)
Marco Cicalese - Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy (email)

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.

Keywords:  Lattice systems, $\Gamma$-convergence, anti-phase boundaries, surface energies, spin systems, binary alloys.
Mathematics Subject Classification:  Primary: 49S05, 49J45, 82B20, 82B24; Secondary: 49M25, 49Q20, 49Q25.

Received: September 2005;      Revised: October 2005;      Published: January 2006.