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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

In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…

Mathematical Physics · Physics 2025-07-30 G. Niccoli , V. Terras

In this paper, we introduce and analyze a new switch operator for the six-vertex model. This operator, derived from the Yang-Baxter equation, allows us to express the partition function with arbitrary boundaries in terms of a base case with…

Combinatorics · Mathematics 2023-03-03 Evelyn Choi , Jadon Geathers , Slava Naprienko

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently…

Mathematical Physics · Physics 2015-07-23 Filippo Colomo , Andrei G. Pronko

We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…

Mathematical Physics · Physics 2010-10-26 K. Palamarchuk , N. Reshetikhin

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

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary…

Statistical Mechanics · Physics 2018-05-11 Ivar Lyberg , Vladimir Korepin , G. A. P. Ribeiro , Jacopo Viti

We consider the six-vertex model with reflecting end boundary condition. We study the asymptotic behavior of the boundary correlations. This asymptotic behavior is used as an input into the Tangent Method in order to derive analytically the…

Mathematical Physics · Physics 2019-11-12 I. R. Passos , G. A. P. Ribeiro

We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the…

Mathematical Physics · Physics 2015-02-23 Pavel Bleher , Karl Liechty

The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…

Condensed Matter · Physics 2009-10-30 P. Zinn-Justin

Four natural boundary statistics and two natural bulk statistics are considered for alternating sign matrices (ASMs). Specifically, these statistics are the positions of the 1's in the first and last rows and columns of an ASM, and the…

Combinatorics · Mathematics 2013-11-01 Roger E. Behrend

We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant…

Mathematical Physics · Physics 2011-02-16 A Caradoc , O Foda , M Wheeler , M Zuparic

In this letter we show the partition function of the 8VSOS model with domain-wall boundaries satisfies the same type of functional equations as its six-vertex model counterpart. We then use these refined functional equations to obtain novel…

Mathematical Physics · Physics 2019-02-13 W. Galleas

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model…

Mathematical Physics · Physics 2015-05-28 Wen-Li Yang , Xi Chen , Jun Feng , Kun Hao , Bo-Yu Hou , Kang-Jie Shi , Yao-Zhong Zhang

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex…

Statistical Mechanics · Physics 2009-11-11 Kazuhiko Minami

We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully…

Statistical Mechanics · Physics 2014-12-09 Chihiro Matsui

We study the eight-vertex model at its free-fermion point. We express a new "switching" symmetry of the model in several forms: partition functions, order-disorder variables, couplings, Kasteleyn matrices. This symmetry can be used to…

Mathematical Physics · Physics 2020-09-23 Paul Melotti

The two point functions, which give the probability that the spins turn down at the boundaries, are studied for the six vertex model on a $2N \times N$ lattice with domain wall boundary condition and left reflecting end. We consider two…

Mathematical Physics · Physics 2010-06-25 Kohei Motegi

We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the…

Mathematical Physics · Physics 2012-09-03 O. Foda , M. Wheeler

For a particular set of Boltzmann weights and a particular boundary condition for the six vertex model in statistical mechanics, we compute explicitly the partition function and show it to be equal to a factorial Schur function, giving a…

Combinatorics · Mathematics 2009-11-01 Peter J. McNamara