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
17425468 (eISSN)
Vol. 2016 8 artikel nr 083106- 083106Subject Categories
Condensed Matter Physics
DOI
10.1088/1742-5468/2016/08/083106