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

Tadahisa Funaki; Yuto Nishijima; Hayate Suda

doi:10.1007/s10955-021-02789-z

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

Tadahisa Funaki^*, Yuto Nishijima, Hayate Suda

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	11
Journal	Journal of Statistical Physics
Volume	184
Issue number	1
DOIs	https://doi.org/10.1007/s10955-021-02789-z
Publication status	Published - 2021 Jul

Keywords

Eight-vertex model
Invariant measure
KPZ equation
Scaling limit

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-021-02789-z

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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.",

keywords = "Eight-vertex model, Invariant measure, KPZ equation, Scaling limit",

author = "Tadahisa Funaki and Yuto Nishijima and Hayate Suda",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Funaki, Tadahisa

AU - Nishijima, Yuto

AU - Suda, Hayate

N1 - Funding Information: 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. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/7

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N2 - 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.

AB - 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.

KW - Eight-vertex model

KW - Invariant measure

KW - KPZ equation

KW - Scaling limit

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

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Keywords

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