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2008

Discretely Holomorphic Parafermions and Integrable Loop Models

Ikhlef, Yacine, Cardy, John

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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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