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Freezing transition in the Ising model without internal contours
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  • Published: November 1999

Freezing transition in the Ising model without internal contours

  • Christian Maes1 &
  • Senya Shlosman2 

Probability Theory and Related Fields volume 115, pages 479–503 (1999)Cite this article

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  • 2 Citations

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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 (h≤h 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.

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. e-mail: Christian.Maes@fys.kuleuven.ac.be, , , , , , BE

    Christian Maes

  2. CPT, Luminy, Marseille and IPPI, Marseille and IPPI, Russian, Academy of Sciences. e-mail: shlosman@cptsu6.univmrs.fr, , , , , , RU

    Senya Shlosman

Authors
  1. Christian Maes
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  2. Senya Shlosman
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Received: 10 November 1998

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Maes, C., Shlosman, S. Freezing transition in the Ising model without internal contours. Probab Theory Relat Fields 115, 479–503 (1999). https://doi.org/10.1007/s004400050246

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  • Issue Date: November 1999

  • DOI: https://doi.org/10.1007/s004400050246

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