Boundary correlation functions of the six-vertex model

Abstract

We consider the six-vertex model on an $N\times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known result for the partition function. In the free fermion case the explicit answers are obtained. The introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings.

20 pages, 2 figures, typos corrected

References in corpus (1)

• Boundary polarization in the six-vertex model

Cited by in corpus (43)

• Inhomogeneous field theory inside the arctic circle
• The arctic curve of the domain-wall six-vertex model
• Arctic curves of the six-vertex model on generic domains: the Tangent Method
• Directed-loop Monte Carlo simulations of vertex models
• Square ice, alternating sign matrices and classical orthogonal polynomials
• On the weighted enumeration of alternating sign matrices and descending plane partitions
• Emptiness formation probability in the domain-wall six-vertex model
• The raise and peel model of a fluctuating interface
• On two-point boundary correlations in the six-vertex model with DWBC
• The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
• The limit shape of large alternating sign matrices
• Thermodynamics of the six-vertex model in an L-shaped domain
• Multiply-refined enumeration of alternating sign matrices
• Inhomogeneous Gaussian Free Field inside the interacting arctic curve
• On the partition function of the six-vertex model with domain wall boundary conditions
• On the correlation functions of the domain wall six vertex model
• Four-vertex Model and Random Tilings
• New enumeration formulas for alternating sign matrices and square ice partition functions
• The density profile of the six vertex model with domain wall boundary conditions
• A doubly-refined enumeration of alternating sign matrices and descending plane partitions
• On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions
• Classical topological order of the Rys F-model and its breakdown in realistic spin ice: Topological sectors of Faraday loops
• The role of orthogonal polynomials in the six-vertex model and its combinatorial applications
• The square-lattice F model revisited: a loop-cluster update scaling study
• Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• Thermodynamic limit of the six-vertex model with reflecting end
• The entropy of the six-vertex model with variety of different boundary conditions
• Generalized emptiness formation probability in the six-vertex model
• Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• On the trigonometric Felderhof model with domain wall boundary conditions
• Integral formulas and antisymmetrization relations for the six-vertex model
• The partition function of the four-vertex model in inhomogeneous external field and trace statistics
• The Functional Method for the Domain-Wall Partition Function
• The factorized F-matrices for arbitrary U(1)^(N-1) integrable vertex models
• The monodromy matrix in the F-basis for arbitrary six-vertex models
• Boundary correlations for the six-vertex model with reflecting end boundary condition
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Boundary one-point function of the rational six-vertex model with partial domain wall boundary conditions: explicit formulas and scaling properties
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• A note on a boundary one point function for the six vertex model with reflecting end
• General scalar products in the arbitrary six-vertex model