Can I read Rigidity of the Interface for Percolation and Random-cluster Models on EtoBox?

Rigidity of the Interface for Percolation and Random-cluster Models by Gielis, Guy; Grimmett, Geoffrey is a scholarly article available to read on EtoBox.

What is Rigidity of the Interface for Percolation and Random-cluster Models about?

We study conditioned random-cluster measures with edge-parameter p and cluster-weighting factor q satisfying q \ge 1. The conditioning corresponds to mixed boundary conditions for a spin model. Interfaces may be defined in the sense of Dobrushin, and these are proved to be `rigid' in the thermodynamic limit, in three dimensions and for sufficiently large values of p. This implies the existence of non-translation-invariant (conditioned) random-cluster measures in three dimensions. The results are valid in the special case q=1, thus indicating a property of three-dimensional percolation not previously noted.

Author

Gielis, Guy; Grimmett, Geoffrey

Published

2001

Language

EN