# Elliptic pfaffians and solvable lattice models

@article{Rosengren2016EllipticPA, title={Elliptic pfaffians and solvable lattice models}, author={Hjalmar Rosengren}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2016}, volume={2016} }

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 eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the…

## 8 Citations

### Elliptic free-fermion model with OS boundary and elliptic Pfaffians

- Mathematics, PhysicsLetters in Mathematical Physics
- 2018

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…

### Elliptic free-fermion model with OS boundary and elliptic Pfaffians

- Mathematics, PhysicsLetters in Mathematical Physics
- 2018

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…

### On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

The transfer matrix of the square-lattice eight-vertex model on a strip with vertical lines and open boundary conditions is investigated. It is shown that for vertex weights that obey the relation…

### Sum rules for the supersymmetric eight-vertex model

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a 2 + ab)(b 2 + ab) = (c 2 + ab)(d 2 + ab) is considered. Its transfer matrix with L = 2n + 1, n ⩾ 0,…

### On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

- Mathematics, Physics
- 2017

The square-lattice eight-vertex model with vertex weights a,b,c,d obeying the relation (a2+ab)(b2+ab)=(c2+ab)(d2+ab) and periodic boundary conditions is considered. It is shown that the transfer…

### On the elliptic 𝔤𝔩2 solid-on-solid model: Functional relations and determinants

- MathematicsJournal of Mathematical Physics
- 2019

In this work, we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group Ep,γ[gl2^] as its underlying symmetry algebra. We elaborate on results previously…

### O ct 2 01 8 Elliptic free-fermion model with OS boundary and elliptic

- Mathematics, Physics
- 2018

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…

### On the elliptic $\mathfrak{gl}_2$ solid-on-solid model: functional relations and determinants

- Mathematics
- 2016

In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $\mathcal{E}_{p, \gamma}[\widehat{\mathfrak{gl}_2}]$ as its underlying symmetry…

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