A simple proof of the stability criterion of Gray and Griffeath


Journal Article

Gray and Griffeath studied attractive nearest neighbor spin systems on the integers having "all 0's" and "all 1's" as traps. Using the contour method, they established a necessary and sufficient condition for the stability of the "all 1's" equilibrium under small perturbations. In this paper we use a renormalized site construction to give a much simpler proof. Our new approach can be used in many situations as a substitute for the contour method. © 1988 Springer-Verlag.

Full Text

Duke Authors

Cited Authors

  • Bramson, M; Durrett, R

Published Date

  • December 1, 1988

Published In

Volume / Issue

  • 80 / 2

Start / End Page

  • 293 - 298

Electronic International Standard Serial Number (EISSN)

  • 1432-2064

International Standard Serial Number (ISSN)

  • 0178-8051

Digital Object Identifier (DOI)

  • 10.1007/BF00356107

Citation Source

  • Scopus