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Fluctuations of the Phase Boundary in the 2D Ising Ferromagnet

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Abstract:

We discuss some statistical properties of the phase boundary in the 2D low-temperature Ising ferromagnet in a box with the two-component boundary conditions. We prove the weak convergence in C[0,1] of measures describing the fluctuations of phase boundaries in the canonical ensemble of interfaces with fixed endpoints and area enclosed below them. The limiting Gaussian measure coincides with the conditional distribution of certain Gaussian process obtained by the integral transformation of the white noise.

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Authors and Affiliations

  1. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova 3“b”, Lviv 290601, Ukraine. E-mail: hryniv@mebm.lviv.ua, , , , , , UA

    O. Hryniv

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  1. R. Dobrushin
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  2. O. Hryniv
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Received: 20 July 1996 / Accepted: 18 February 1997

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Dobrushin , R., Hryniv, O. Fluctuations of the Phase Boundary in the 2D Ising Ferromagnet . Comm Math Phys 189, 395–445 (1997). https://doi.org/10.1007/s002200050209

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  • DOI: https://doi.org/10.1007/s002200050209

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