English

Discretely Holomorphic Parafermions and Integrable Loop Models

Mathematical Physics 2009-11-13 v2 Statistical Mechanics math.MP

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.

Keywords

Cite

@article{arxiv.0810.5037,
  title  = {Discretely Holomorphic Parafermions and Integrable Loop Models},
  author = {Yacine Ikhlef and John Cardy},
  journal= {arXiv preprint arXiv:0810.5037},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:35:42.987Z