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Elliptic pfaffians and solvable lattice models

Hjalmar Rosengren (Institutionen för matematiska vetenskaper, matematik)
Journal of Statistical Mechanics: Theory and Experiment (1742-5468). Vol. 2016 (2016), 8, p. artikel nr 083106.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: integrable spin chains and vertex models, solvable lattice models, anisotropic heisenberg chain, 8-vertex model, symmetric functions, determinant, squares, sums, statistics, identities, equation, formula, Mechanics, Physics



Denna post skapades 2016-10-25. Senast ändrad 2016-11-21.
CPL Pubid: 244049

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Den kondenserade materiens fysik

Chalmers infrastruktur