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Stochastic Eight-Vertex Model, its Invariant Measures and KPZ Limit

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Abstract

We introduce a stochastic eight-vertex model motivated by the eight-vertex model in statistical mechanics. We study its invariant measures under a certain balance condition for the creation and annihilation probabilities of particles. We also discuss its scaling limits, that is, the hydrodynamic limit, and the linear and nonlinear fluctuations rather formally. We especially obtain a new type of KPZ-Burgers equation in the nonlinear limit.

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Acknowledgements

T. Funaki was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Researches (A) 18H03672 and (S) 16H06338. H. Suda was supported by JSPS KAKENHI Grant Number JP19J11268 and the Program for Leading Graduate Schools, MEXT, Japan.

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Author notes

  1. Yuto Nishijima

    Present address: DATUM STUDIO Co. Ltd., Toranomon Hills Business Tower 1-17-1 Toranomon, Minato-ku, Tokyo, 105-6490, Japan

  2. Hayate Suda

    Present address: Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

Authors and Affiliations

  1. Department of Mathematics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Tadahisa Funaki & Yuto Nishijima

  2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Hayate Suda

Authors
  1. Tadahisa Funaki
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  2. Yuto Nishijima
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  3. Hayate Suda
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Correspondence to Tadahisa Funaki.

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Communicated by Herbert Spohn.

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Funaki, T., Nishijima, Y. & Suda, H. Stochastic Eight-Vertex Model, its Invariant Measures and KPZ Limit. J Stat Phys 184, 11 (2021). https://doi.org/10.1007/s10955-021-02789-z

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  • DOI: https://doi.org/10.1007/s10955-021-02789-z

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