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Journal of Statistical Physics

, Volume 174, Issue 1, pp 1–27 | Cite as

Arctic Curve of the Free-Fermion Six-Vertex Model in an L-Shaped Domain

  • F. Colomo
  • A. G. PronkoEmail author
  • A. Sportiello
Article

Abstract

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions, in the case of free-fermion vertex weights. We describe how the recently developed ‘Tangent method’ can be used to determine the form of the arctic curve. The obtained result is in agreement with numerics.

Keywords

Vertex models Domain wall boundary conditions Limit shape phenomena Arctic curves Tangent method Log-gas representations 

Notes

Acknowledgements

We are grateful to A. Abanov, S. Chhita and F. Franchini for interesting discussions. We are indebted to B. Wieland for sharing with us the code for generating uniformly sampled alternating-sign matrices. We thank the Simons Center for Geometry and Physics (SCGP, Stony Brook), research program on ‘Statistical Mechanics and Combinatorics’ and the Galileo Galilei Institute for Theoretical Physics (GGI, Florence), research programs on ‘Statistical Mechanics, Integrability and Combinatorics’ and ‘Entanglement in Quantum Systems’, for hospitality and support at some stage of this work. FC is grateful to LIPN, équipe Calin at Université Paris 13, for hospitality and support at some stage of this work. AGP and AS are grateful to INFN, Sezione di Firenze for hospitality and support at some stage of this work. AGP acknowledges partial support from the Russian Science Foundation, Grant #18-11-00297.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.INFN, Sezione di FirenzeSesto FiorentinoItaly
  2. 2.Steklov Mathematical InstituteSt. PetersburgRussia
  3. 3.LIPN, and CNRS, Université Paris 13, Sorbonne Paris CitéVilletaneuseFrance

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