Integrability of Limit Shapes of the Six Vertex Model

The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the six vertex model on a cylinder. This suggests that the limit shape equation is an integrable PDE with gradient constraints. At...

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Bibliographic Details
Published in:Communications in mathematical physics 2017-12, Vol.356 (2), p.535-565
Main Authors: Reshetikhin, Nicolai, Sridhar, Ananth
Format: Article
Language:English
Subjects:
Burgers equation
Classical and Quantum Gravitation
Complex Systems
Cylinders
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the six vertex model on a cylinder. This suggests that the limit shape equation is an integrable PDE with gradient constraints. At the free fermionic point this equation becomes the complex Burgers equation.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-017-2983-x