Chaotic Size Dependence in the Ising Model with Random Boundary Conditions
2002, v.8, Issue 3, 479-508
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.
Keywords: random boundary conditions,metastates,contour models,local limit theorem,central limit theorem