Discretely Holomorphic Parafermions in Lattice Z(N) Models

Details Discretely Holomorphic Parafermions in Lattice Z(N) Models Discretely Holomorphic Parafermions in Lattice Z(N) Models

2007-08-28

arxiv.org/abs/0708.3772v3

J.Phys.A40:14703-14713,2008

Physics

Mathematical Physics

v2: minor corrections; v3: published version - minor corrections and reference added

Scientific paper

10.1088/1751-8113/40/49/006

We construct lattice parafermions - local products of order and disorder operators - in nearest-neighbor Z(N) models on regular isotropic planar lattices, and show that they are discretely holomorphic, that is they satisfy discrete Cauchy-Riemann equations, precisely at the critical Fateev-Zamolodchikov (FZ) integrable points. We generalize our analysis to models with anisotropic interactions, showing that, as long as the lattice is correctly embedded in the plane, such discretely holomorphic parafermions exist for particular values of the couplings which we identify as the anisotropic FZ points. These results extend to more general inhomogeneous lattice models as long as the covering lattice admits a rhombic embedding in the plane.

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