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Discretely holomorphic parafermions and integrable loop models

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, w...

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Journal:
Journal of Physics A: Mathematical and Theoretical
Volume:
42
Issue:
10
Publication date:
2009-01-01
DOI:
EISSN:
1751-8121
ISSN:
1751-8113
URN:
uuid:959b2cb1-d6c4-4486-884c-6639aedea65c
Source identifiers:
240757
Local pid:
pubs:240757
Language:
English

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