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Integrability of Limit Shapes of the Six Vertex Model

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arxiv 1510.01053 v1 pith:SS2B5O7Y submitted 2015-10-05 math-ph cond-mat.stat-mechhep-thmath.MP

Nicolai Reshetikhin , Ananth Sridhar This is my paper · ORCID
classification math-phcond-mat.stat-mechhep-thmath.MP
keywords equationlimitmodelshapevertexbecomesburgerscommuting
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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 6-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.

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    nlin.SI 2026-08 conditional novelty 7.0 of 10

    Liouville integrability conditions for monomial charge densities reduce to a negative Pell equation, generating an infinite set of commuting conserved charges for a new dispersionless Hamiltonian model.

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