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arXiv · 1202.6265

Discretely holomorphic parafermions and integrable boundary conditions

Yacine Ikhlef
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Abstract

In two-dimensional statistical models possessing a discretely holomorphic parafermion, we introduce a modified discrete Cauchy-Riemann equation on the boundary of the domain, and we show that the solution of this equation yields integrable boundary Boltzmann weights. This approach is applied to (i) the square-lattice O(n) loop model, where the exact locations of the special and ordinary transitions are recovered, and (ii) the Fateev-Zamolodchikov $Z_N$ spin model, where a new rotation-invariant, integrable boundary condition is discovered for generic $N$.

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Yacine Ikhlef. 2012-02-28. Discretely holomorphic parafermions and integrable boundary conditions. https://doi.org/10.1088/1751-8113/45/26/265001

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