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May 2022 Critical prewetting in the 2d Ising model
Dmitry Ioffe, Sébastien Ott, Senya Shlosman, Yvan Velenik
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Ann. Probab. 50(3): 1127-1172 (May 2022). DOI: 10.1214/21-AOP1555

Abstract

In this paper, we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N×N rectangular box with a boundary condition inducing the coexistence of the + phase in the bulk and a layer of − phase along the bottom wall. The presence of an external magnetic field of intensity h=λ/N (for some fixed λ>0) makes the layer of − phase unstable. For any β>βc, we prove that, under a diffusing scaling by N2/3 horizontally and N1/3 vertically, the interface separating the layer of unstable phase from the bulk phase weakly converges to an explicit Ferrari–Spohn diffusion.

Funding Statement

The research of D. Ioffe was partially supported by Israeli Science Foundation grant 765/18.
S. Ott thanks the university Roma Tre for its hospitality and is supported by the Swiss NSF through an early PostDoc.Mobility Grant.
The research of S. Shlosman was partially supported by the Russian Science Foundation (project No. 20-41-09009).
The research of Y. Velenik was partially supported by the Swiss NSF through the NCCR SwissMAP.

Acknowledgments

The authors are grateful to Shirshendu Ganguly and Reza Gheissari for sending them their preprint [17]. They also thank the referees for their careful reading and suggestions that have improved the presentation of this work.

Additional address of the third author is CPT, Aix Marseille Univ, Universite de Toulon, CNRS, France.

Citation

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Dmitry Ioffe. Sébastien Ott. Senya Shlosman. Yvan Velenik. "Critical prewetting in the 2d Ising model." Ann. Probab. 50 (3) 1127 - 1172, May 2022. https://doi.org/10.1214/21-AOP1555

Information

Received: 1 November 2020; Revised: 1 July 2021; Published: May 2022
First available in Project Euclid: 27 April 2022

Digital Object Identifier: 10.1214/21-AOP1555

Subjects:
Primary: 60K35 , 82B20 , 82B24

Keywords: critical prewetting , Ferrari–Spohn diffusion , Interface , invariance principle , Ising model

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 3 • May 2022
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