Aernout C.D. van Enter, Igor Medved, Karel Netocny
Chaotic Size Dependence in the Ising Model with Random Boundary
Conditions
(374K, postscript )
ABSTRACT. 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.