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We study numerically the two-point correlation functions of height functions in the six-vertex model with domain wall boundary conditions. The correlation functions and the height functions are computed by the Markov chain Monte-Carlo…

Statistical Mechanics · Physics 2020-12-10 Pavel Belov , Nicolai Reshetikhin

The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation…

Mathematical Physics · Physics 2012-07-20 F. Colomo , A. G. Pronko

Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González Ruiz

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with…

Mathematical Physics · Physics 2025-01-29 Kohei Motegi

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to…

Mathematical Physics · Physics 2017-06-28 Rouven Frassek

We study a class of models in which $N$ flavors of massless fermions on the half line are coupled by an arbitrary orthogonal matrix to $N$ rotors living on the boundary. Integrating out the rotors, we find the exact partition function and…

High Energy Physics - Theory · Physics 2009-10-28 Ali Yegulalp

The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…

Mathematical Physics · Physics 2009-11-23 F. Colomo , A. G. Pronko

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…

Mathematical Physics · Physics 2016-04-20 W. Galleas

In this article, we show that, in the free-fermion regime of the six-vertex model, all $k$-point correlation functions of vertex types admit a determinantal representation: \begin{align*} \mathbb{P}\Bigg( \bigcap_{p=1}^k \{ \text{vertex at…

Probability · Mathematics 2025-12-17 Samuel G. G. Johnston , Rohan Shiatis

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function,…

Mathematical Physics · Physics 2024-12-03 Filippo Colomo , Andrei G. Pronko

The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…

Statistical Mechanics · Physics 2020-11-23 Nikolay Bogoliubov , Cyril Malyshev

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…

Mathematical Physics · Physics 2009-11-07 J. de Gier , V. Korepin

We study the partition function for the three-colour model with domain wall boundary conditions. We express it in terms of certain special polynomials, which can be constructed recursively. Our method generalizes Kuperberg's proof of the…

Combinatorics · Mathematics 2014-06-16 Hjalmar Rosengren

The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…

Mathematical Physics · Physics 2022-05-04 Linnea Hietala

The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this…

Mathematical Physics · Physics 2009-11-23 F. Colomo , A. G. Pronko

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…

Statistical Mechanics · Physics 2007-05-23 P. Zinn-Justin

The free fermion condition of the six-vertex model provides a 5 parameter sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing…

Statistical Mechanics · Physics 2009-10-31 R. Brak , A. Owczarek

We establish bounds on the decay of time-dependent multipoint correlation functionals of one-dimensional quasi-free fermions in terms of the decay properties of their two-point function. At a technical level, this is done with the help of…

Mathematical Physics · Physics 2016-04-20 Robert Sims , Simone Warzel

The six-vertex model is an important toy-model in statistical mechanics for two-dimensional ice with a natural parameter $\Delta$. When $\Delta = 0$, the so-called free-fermion point, the model is in natural correspondence with domino…

Probability · Mathematics 2022-07-08 Arvind Ayyer , Sunil Chhita , Kurt Johansson

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…

Mesoscale and Nanoscale Physics · Physics 2008-11-26 Bertrand Eynard