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Probability Theory and Related Fields

, Volume 115, Issue 4, pp 479–503 | Cite as

Freezing transition in the Ising model without internal contours

  • Christian Maes
  • Senya Shlosman

Abstract.

We consider the low temperature Ising model in a uniform magnetic field h > 0 with minus boundary conditions and conditioned on having no internal contours. This simple contour model defines a non-Gibbsian spin state. For large enough magnetic fields (h >: h c ) this state is concentrated on the single spin configuration of all spins up. For smaller values (hh c ), the spin state is non-trivial. At the critical point h c ≠ 0 the magnetization jumps discontinuously. Freezing provides also an example of a translation invariant weakly Gibbsian state which is not almost Gibbsian.

Mathematical Subject Classification (1991): 60G, 82B20, 82B31, 82B26 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christian Maes
    • 1
  • Senya Shlosman
    • 2
  1. 1.Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. e-mail: Christian.Maes@fys.kuleuven.ac.beBE
  2. 2.CPT, Luminy, Marseille and IPPI, Marseille and IPPI, Russian, Academy of Sciences. e-mail: shlosman@cptsu6.univmrs.frRU

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