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Related papers: Six-Vertex Model with Domain Wall Boundary Conditi…

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Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization')…

Statistical Mechanics · Physics 2009-11-07 N. M. Bogoliubov , A. V. Kitaev , M. B. Zvonarev

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…

Mathematical Physics · Physics 2024-01-10 S. Belliard , R. A. Pimenta , N. A. Slavnov

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

We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both…

High Energy Physics - Theory · Physics 2020-07-24 Zoltan Bajnok , Jesper Lykke Jacobsen , Yunfeng Jiang , Rafael I. Nepomechie , Yang Zhang

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…

Statistical Mechanics · Physics 2007-05-23 Tetsuo Deguchi

We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an…

Combinatorics · Mathematics 2020-05-15 Philippe Di Francesco , Emmanuel Guitter

We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles…

Statistical Mechanics · Physics 2017-05-10 Ivar Lyberg , Vladimir Korepin , Jacopo Viti

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 continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified…

Mathematical Physics · Physics 2026-03-11 Matthieu Cornillault , Samuel Belliard

The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general…

Mathematical Physics · Physics 2021-03-17 Vladimir V. Bazhanov , Gleb A. Kotousov , Sergii M. Koval , Sergei L. Lukyanov

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite…

High Energy Physics - Theory · Physics 2008-12-22 Charles Nash , Denjoe O'Connor

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…

Statistical Mechanics · Physics 2016-10-04 Leticia F. Cugliandolo , Giuseppe Gonnella , Alessandro Pelizzola

We consider the six-vertex model with the rational weights on an $s\times N$ square lattice, $s\leq N$, with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are…

Mathematical Physics · Physics 2022-01-13 Mikhail D. Minin , Andrei G. Pronko

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer…

Statistical Mechanics · Physics 2009-10-30 V. Popkov , Doochul Kim , H. Y. Huang , F. Y. Wu

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…

Superconductivity · Physics 2009-11-13 Benoit Vanderheyden , A D Jackson

We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$…

Mathematical Physics · Physics 2017-06-08 Kohei Motegi

The free energies of six-vertex models on general domain D with various boundary conditions are investigated with the use of the n-equivalence relation which classifies the thermodynamic limit properties. It is derived that the free energy…

Statistical Mechanics · Physics 2008-05-10 Kazuhiko Minami

A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…

Mathematical Physics · Physics 2015-05-19 Kohei Motegi

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 study the thermodynamic limit of the six-vertex model with domain wall boundary and reflecting end. We evaluated the partition function explicitly in special cases. We calculated the homogeneous limit of the Tsuchiya determinant formula…

Statistical Mechanics · Physics 2015-01-14 G. A. P. Ribeiro , V. E. Korepin