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arXiv · 0810.5037

Discretely Holomorphic Parafermions and Integrable Loop Models

Yacine Ikhlef·John Cardy
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Abstract

We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic (they satisfy a lattice version of the Cauchy-Riemann equations) as long as the Boltzmann weights satisfy certain linear constraints. In the cases considered, the weights then also satisfy the critical Yang-Baxter equations, with the spectral parameter being related linearly to the angle of the elementary rhombus.

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Yacine Ikhlef, John Cardy. 2009-02-23. Discretely Holomorphic Parafermions and Integrable Loop Models. https://doi.org/10.1088/1751-8113%2F42%2F10%2F102001

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