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Currents in the dilute $O(n=1)$ model

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arxiv 1510.02721 v2 pith:7I3QJFEY submitted 2015-10-09 math-ph cond-mat.stat-mechmath.MPnlin.SI

G. Z. Fehér , B. Nienhuis This is my paper · ORCID
classification math-phcond-mat.stat-mechmath.MPnlin.SI
keywords modellatticediluteexpressionsboundary-to-boundarychaincriticalcurrent
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abstract

In the framework of an inhomogeneous solvable lattice model, we derive exact expressions for a boundary-to-boundary current on a lattice of finite width. The model we use is the dilute $O(n=1)$ loop model, related to the Izergin-Korepin spin-1 chain and the critical site percolation on the triangular lattice. Our expressions are derived based on solutions of the $q$-Knizhnik-Zamolodchikov equations, and recursion relations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modular covariant torus partition functions of dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models

    math-ph 2025-01 conditional novelty 7.0 of 10

    For all coprime (p,p'), the dense A_1^(1) and dilute A_2^(2) loop models are conjectured to have identical torus conformal partition functions, supporting a common logarithmic universality class.

  2. Rational symmetric functions from the Izergin-Korepin 19-vertex model

    math.CO 2024-12 conditional novelty 7.0 of 10

    New rational symmetric functions are constructed from the 19-vertex model, with Cauchy identities, stable limits, and a symmetrization formula over 2-permutations.

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