Elliptic pfaffians and solvable lattice models
Journal article, 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

Author

Hjalmar Rosengren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Statistical Mechanics: Theory and Experiment

1742-5468 (ISSN)

Vol. 2016 8 artikel nr 083106-

Subject Categories

Condensed Matter Physics

DOI

10.1088/1742-5468/2016/08/083106

More information

Created

10/8/2017