2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56847We 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.LaTeX2e, 30 pages, no figuresMathematical PhysicsProbability82B20, 82B44 (Primary) 60F05, 60K35 (Secondary)text