A simple proof of the stability criterion of Gray and Griffeath
\textit{L. Gray} and \textit{D. Griffeath} [Ann. Probab. 10, 67-85 (1982; Zbl 0483.60090)] studied attractive nearest neighbor spin systems on the integers having ``all 0's'' and ``all 1's'' as traps. Using the contour methods, 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.
attractive nearest neighbor spin systems
scientific article; zbMATH DE number 4043009