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Level set representation for the Gibbs states of the ferromagnetic ising model
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  • Published: June 1991

Level set representation for the Gibbs states of the ferromagnetic ising model

  • Yasunari Higuchi1 

Probability Theory and Related Fields volume 90, pages 203–221 (1991)Cite this article

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Summary

We prove the existence of a real valued random field with parameters in thed-dimensional cubic lattice, such that the distribution of the level set of this random field is a Gibbs state for the nearest neighbour ferromagnetic Ising model. Using this, we prove the continuity of the percolation probability with respect to the parameter (β,h) in the uniqueness region except on the critical curve Γ c ={(β,h c (β))}, whereh c(β) is the critical level of the external field above which percolation takes place.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Kobe University, Rokko, 657, Kobe, Japan

    Yasunari Higuchi

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  1. Yasunari Higuchi
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Additional information

Supported in part by JSPS, BiBoS, Grant in Aid for Cooperative research no. 62303006 and Grant in Aid for Scientific Research no. 63540168

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Higuchi, Y. Level set representation for the Gibbs states of the ferromagnetic ising model. Probab. Th. Rel. Fields 90, 203–221 (1991). https://doi.org/10.1007/BF01192162

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  • Received: 04 July 1990

  • Revised: 16 April 1991

  • Issue Date: June 1991

  • DOI: https://doi.org/10.1007/BF01192162

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Keywords

  • Stochastic Process
  • Probability Theory
  • Random Field
  • External Field
  • Mathematical Biology
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