Integrability of Limit Shapes of the Six Vertex Model
classification
🧮 math-ph
cond-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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