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Название: On the Ising Model with Random Boundary Condition
Авторы: van Enter A.C.D., Netocny K., Schaap H.G.
Journal of Statistical Physics, Vol. 118, Nos. 5/6, March 2005. p. 997-1056.
The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the '+' and '—' phases are the only almost sure limit Gibbs measures, assuming that the limit is taken along a sparse enough sequence of squares. In particular, we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces. In order to exclude mixtures as possible limit points, a detailed multi-scale contour analysis is performed.