Chaotic Size Dependence in the Ising Model with Random Boundary Conditions

A.C.D. van Enter, I. Medved’, K. Netočný

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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.
Original languageEnglish
Pages (from-to) 479-508
Number of pages31
JournalMarkov Processes and Related Fields
Issue number3
Publication statusPublished - 2002


  • local- and central-limit theorems
  • contour models
  • metastates
  • random boundary conditions

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