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Surface order large deviations for Ising, Potts and percolation models
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  • Published: December 1996

Surface order large deviations for Ising, Potts and percolation models

  • Agoston Pisztora1 nAff2 

Probability Theory and Related Fields volume 104, pages 427–466 (1996)Cite this article

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Summary

We derive uniform surface order large deviation estimates for the block magnetization in finite volume Ising (or Potts) models with plus or free (or a combination of both) boundary conditions in the phase coexistence regime ford≧3. The results are valid up to a limit of slab-thresholds, conjectured to agree with the critical temperature. Our arguments are based on the renormalization of the random cluster model withq≧1 andd≧3, and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability. The results are new even for the case of independent percolation (q=1). As a byproduct of our methods, we obtain further results in the FK model concerning semicontinuity (inp andq) of the percolation probability, the second largest cluster in a box and the tail of the finite cluster size distribution.

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Author notes
  1. Agoston Pisztora

    Present address: Department of Mathematics, Harvard University, 1 Oxford Street, 02138, Cambridge, MA, USA

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    Agoston Pisztora

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  1. Agoston Pisztora
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Pisztora, A. Surface order large deviations for Ising, Potts and percolation models. Probab. Th. Rel. Fields 104, 427–466 (1996). https://doi.org/10.1007/BF01198161

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  • Received: 19 December 1994

  • Revised: 20 July 1995

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01198161

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Mathematics Subject Classification (1991)

  • 60F10
  • 60K35
  • 82B20
  • 82B43
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