Abstract
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.
Original language | English (US) |
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Pages (from-to) | 293-298 |
Number of pages | 6 |
Journal | Probability Theory and Related Fields |
Volume | 80 |
Issue number | 2 |
DOIs | |
State | Published - Dec 1988 |