In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be characterized by two phases separated by an interface. The macroscopic surface tension at this interface is defined through a first-passage percolation formula, related to the chemical distance on the lattice Z^2. We also show a continuity result, that is the homogenization of rigid spin system is a limit case of the elliptic random homogenization.
Variational problems with percolation: rigid spin systems / Scilla, Giovanni. - In: ADVANCES IN MATHEMATICAL SCIENCES AND APPLICATIONS. - ISSN 1343-4373. - 23:(2013), pp. 187-207.
Variational problems with percolation: rigid spin systems
Giovanni Scilla
2013
Abstract
In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be characterized by two phases separated by an interface. The macroscopic surface tension at this interface is defined through a first-passage percolation formula, related to the chemical distance on the lattice Z^2. We also show a continuity result, that is the homogenization of rigid spin system is a limit case of the elliptic random homogenization.| File | Dimensione | Formato | |
|---|---|---|---|
|
Rigidspin_rev.pdf
solo utenti autorizzati
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
357.48 kB
Formato
Adobe PDF
|
357.48 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
