We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.
|Number of pages||31|
|Journal||Markov Processes and Related Fields|
|Publication status||Published - 2002|
- local- and central-limit theorems
- contour models
- random boundary conditions