## 29 Citations

### Partial differential equations from integrable vertex models

- Mathematics, Computer Science
- 2014

A mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations for the Uq[sl(2)] invariant six-vertex model is proposed.

### New differential equations in the six-vertex model

- Mathematics
- 2016

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…

### Functional relations in nineteen-vertex models with domain-wall boundaries

- MathematicsJournal of Mathematical Physics
- 2019

This work is concerned with functional properties shared by partition functions of nineteen-vertex models with domain-wall boundary conditions. In particular, we describe both Izergin-Korepin and…

### from integrable vertex models

- Mathematics, Computer Science
- 2014

A mechanism for converting the spectral problem for vertex models transfer matrices into the solution of certain linear partial dierential equations for invariant six-vertex models is proposed.

### New determinants in the 8VSOS model with domain-wall boundaries

- Mathematics
- 2018

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…

### Scalar Product of Bethe Vectors from Functional Equations

- Mathematics
- 2012

In this work the scalar product of Bethe vectors for the six-vertex model is studied by means of functional equations. The scalar products are shown to obey a system of functional equations…

### Scalar Product of Bethe Vectors from Functional Equations

- MathematicsCommunications in Mathematical Physics
- 2014

In this work the scalar product of Bethe vectors for the six-vertex model is studied by means of functional equations. The scalar products are shown to obey a system of functional equations…

### The Functional Method for the Domain-Wall Partition Function

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2018

We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method using the simplest example: the computation of the…

## 35 References

### Functional relations for the six-vertex model with domain wall boundary conditions

- Mathematics, Physics
- 2010

In this work we demonstrate that the Yang–Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six-vertex model with domain wall boundary…

### Multiple integral representation for the trigonometric SOS model with domain wall boundaries

- Mathematics, Physics
- 2012

### The SOS model partition function and the elliptic weight functions

- Mathematics
- 2008

We generalized a recent observation (Khoroshkin and Pakuliak 2005 Theor. Math. Phys. 145 1373) that the partition function of the six-vertex model with domain wall boundary conditions can be obtained…

### Partition function of the eight-vertex model with domain wall boundary condition

- Physics, Mathematics
- 2009

We derive the recursive relations of the partition function for the eight-vertex model on an N×N square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the…

### The eight-vertex model and Painlevé VI equation II: eigenvector results

- Mathematics
- 2010

We study a special anisotropic -model on a periodic chain of an odd length and conjecture exact expressions for certain components of the ground state eigenvectors. The results are written in terms…

### Three-coloring statistical model with domain wall boundary conditions: Functional equations

- Mathematics
- 2008

We consider the Baxter three-coloring model with boundary conditions of the domain wall type. In this case, it can be proved that the partition function satisfies some functional equations similar to…

### An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices

- MathematicsAdv. Appl. Math.
- 2009