On the partition function of the six-vertex model with domain wall boundary conditions

Abstract

The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ``reconstruction'' formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.

typos corrected

References in corpus (11)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Fredholm Determinants, Differential Equations and Matrix Models
• Local statistics for random domino tilings of the Aztec diamond
• Thermodynamic limit of the Six-Vertex Model with Domain Wall Boundary Conditions
• Random Domino Tilings and the Arctic Circle Theorem
• Algebraic Aspects of Bethe-Ansatz
• Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
• Proof of the Refined Alternating Sign Matrix Conjecture
• Boundary correlation functions of the six-vertex model
• Boundary polarization in the six-vertex model
• Continuous space-time symmetries in a lattice field theory

Cited by in corpus (12)

• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• On the weighted enumeration of alternating sign matrices and descending plane partitions
• Functional relations for the six vertex model with domain wall boundary conditions
• Multiply-refined enumeration of alternating sign matrices
• New enumeration formulas for alternating sign matrices and square ice partition functions
• Thermodynamic limit of the six-vertex model with reflecting end
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Symmetry classes of alternating sign matrices in the nineteen-vertex model
• Boundary correlations for the six-vertex model with reflecting end boundary condition
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• Multiple Meixner-Pollaczek polynomials and the six-vertex model
• New proofs of determinant evaluations related to plane partitions