Electronic Journal of Probability

One-dimensional Random Field Kac's Model: Localization of the Phases

Marzio Cassandro, Enza Orlandi, Pierre Picco, and Maria Eulalia Vares

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We study the typical profiles of a one dimensional random field Kac model, for values of the temperature and magnitude of the field in the region of two absolute minima for the free energy of the corresponding random field Curie Weiss model. We show that, for a set of realizations of the random field of overwhelming probability, the localization of the two phases corresponding to the previous minima is completely determined. Namely, we are able to construct random intervals tagged with a sign, where typically, with respect to the infinite volume Gibbs measure, the profile is rigid and takes, according to the sign, one of the two values corresponding to the previous minima. Moreover, we characterize the transition from one phase to the other. The analysis extends the one done by Cassandro, Orlandi and Picco in [13].

Article information

Electron. J. Probab., Volume 10 (2005), paper no. 24, 786-864.

Accepted: 14 July 2005
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B43: Percolation [See also 60K35]

Phase transition random walk random environment Kac potential

This work is licensed under aCreative Commons Attribution 3.0 License.


Cassandro, Marzio; Orlandi, Enza; Picco, Pierre; Vares, Maria Eulalia. One-dimensional Random Field Kac's Model: Localization of the Phases. Electron. J. Probab. 10 (2005), paper no. 24, 786--864. doi:10.1214/EJP.v10-263. https://projecteuclid.org/euclid.ejp/1464816825

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