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We introduce and study a class of partition functions of an elliptic free-fermionic face model. We study the partition functions with a triangular boundary using the off-diagonal $K$-matrix at the boundary (OS boundary), which was…

Mathematical Physics · Physics 2019-03-08 Kohei Motegi

In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…

Mathematical Physics · Physics 2015-11-24 J. Lamers

We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the…

Mathematical Physics · Physics 2019-08-21 I. R. Passos , G. A. P. Ribeiro

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.

Mathematical Physics · Physics 2011-02-16 A Caradoc , O Foda , N Kitanine

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set…

Combinatorics · Mathematics 2015-05-13 Jean-Christophe Aval

Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use…

Mathematical Physics · Physics 2011-08-02 Kohei Motegi

In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of the model in the thermodynamic limit. We consider the same…

Mathematical Physics · Physics 2015-05-13 A. V. Razumov , Yu. G. Stroganov

We propose an (essentially combinatorial) approach to the correlation functions of the domain wall six vertex model. We reproduce the boundary 1-point function determinant expression of Bogoliubov, Pronko and Zvonarev, then use that as a…

Mathematical Physics · Physics 2015-10-21 Omar Foda , Ian Preston

The determinantal form of the partition function of the 6-vertex model with domain wall boundary conditions was given by Izergin. It is known that for a special value of the crossing parameter the partition function reduces to a Schur…

Combinatorics · Mathematics 2014-02-20 Tiago Fonseca , Ferenc Balogh

A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of…

High Energy Physics - Theory · Physics 2016-09-06 Boguslaw Broda , Malgorzata Bakalarska

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

In this paper, we introduce a class of colored stochastic vertex models with U-turn right boundary. The vertex weights in the models satisfy the Yang-Baxter equations and the reflection equation. Based on these equations, we derive…

Probability · Mathematics 2024-01-17 Chenyang Zhong

We study the ground state of the boundary Izergin-Korepin model. The boundary Izergin-Korepin model is defined by so-called $R$-matrix and $K$-matrix for $U_q(A_2^{(2)})$ which satisfy Yang-Baxter equation and boundary Yang-Baxter equation…

Exactly Solvable and Integrable Systems · Physics 2019-02-04 Takeo Kojima

We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation…

Mathematical Physics · Physics 2020-06-23 Luigi Cantini , Filippo Colomo , Andrei G. Pronko

We investigate the $K$-theoretic Gysin map for type $A$ partial flag bundles from the viewpoint of integrability. We introduce several types of partition functions for one version of $q=0$ degeneration of $U_q(\widehat{sl_n})$ vertex models…

Mathematical Physics · Physics 2022-10-21 Kohei Motegi

A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant…

Mathematical Physics · Physics 2008-12-16 A. V. Razumov , Yu. G. Stroganov

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.

High Energy Physics - Theory · Physics 2009-09-25 Robert P. Langlands , Marc-Andre Lewis , Yvan Saint-Aubin

We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…

High Energy Physics - Theory · Physics 2022-10-19 So Matsuura , Kazutoshi Ohta

We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model…

Combinatorics · Mathematics 2020-12-07 Sylvie Corteel , Andrew Gitlin , David Keating , Jeremy Meza

We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the…

Mathematical Physics · Physics 2016-09-21 Hjalmar Rosengren