Discretely Holomorphic Parafermions and Integrable Loop Models

Details Discretely Holomorphic Parafermions and Integrable Loop Models Discretely Holomorphic Parafermions and Integrable Loop Models

2008-10-28

arxiv.org/abs/0810.5037v2

J. Phys. A: Math. Theor. 42 (2009) 102001

Physics

Mathematical Physics

13 pages, 7 figures Added 2 references, corrected minor typos

Scientific paper

10.1088/1751-8113/42/10/102001

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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