Interface Fluctuations in Non Equilibrium Stationary States: The SOS Approximation

Abstract

We study the 2d stationary fluctuations of the interface in the SOS approximation of the non equilibrium stationary state found in De Masi et al. (J Stat Phys 175:203–221, 2019). We prove that the interface fluctuations are of order \(N^{1/4}\), N the size of the system. We also prove that the scaling limit is a stationary Ornstein–Uhlenbeck process.

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Acknowledgements

We thank S. Shlosman for helpful discussions. A.DM thanks very warm hospitality at the University of Paris-Dauphine where part of this work was performed. This work was partially supported by ANR-15-CE40-0020-01 grant LSD.

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Correspondence to Anna De Masi.

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Dedicated to Joel for his important contributions to the theory of phase transition and interfaces.

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Communicated by Michael Aizenman.

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De Masi, A., Merola, I. & Olla, S. Interface Fluctuations in Non Equilibrium Stationary States: The SOS Approximation. J Stat Phys 180, 414–426 (2020). https://doi.org/10.1007/s10955-019-02450-w

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Keywords

  • Non equilibrium stationary states
  • Interfaces
  • SOS model