New differential equations in the six-vertex model

Abstract

This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated Knizhnik-Zamolodchikov equation. The analysis of our PDEs naturally produces a family of novel determinant representations for the model's partition function.

14 pages; v2: minor changes, added reference, accepted for publication in JSTAT

References in corpus (5)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Reflection algebra and functional equations
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Functional relations and the Yang-Baxter algebra
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Cited by in corpus (5)

• Elliptic solid-on-solid model's partition function as a single determinant
• The Functional Method for the Domain-Wall Partition Function
• Six-vertex model and non-linear differential equations I. Spectral problem
• Functional relations in nineteen-vertex models with domain-wall boundaries
• Domain-wall boundaries through non-diagonal twists in the six-vertex model