Elliptic pfaffians and solvable lattice models
Artikel i vetenskaplig tidskrift, 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 supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.

formula

Mechanics

Physics

determinant

integrable spin chains and vertex models

symmetric functions

statistics

sums

squares

anisotropic heisenberg chain

identities

solvable lattice models

8-vertex model

equation

Författare

Hjalmar Rosengren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Statistical Mechanics: Theory and Experiment

1742-5468 (ISSN)

Vol. 2016 8 artikel nr 083106-

Ämneskategorier

Den kondenserade materiens fysik

DOI

10.1088/1742-5468/2016/08/083106

Mer information

Skapat

2017-10-08