Variational problems with percolation: rigid spin systems
Functional Analysis
2014-07-28 v1 Mathematical Physics
math.MP
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 square lattice. We also show a continuity result, that is the homogenization of rigid spin system is a limit case of the elliptic random homogenization.
Cite
@article{arxiv.1407.6926,
title = {Variational problems with percolation: rigid spin systems},
author = {G. Scilla},
journal= {arXiv preprint arXiv:1407.6926},
year = {2014}
}
Comments
21 pages, 2 figures