Integrability as a consequence of discrete holomorphicity: loop models

In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the conditions for integrability, namely, the inversion and Yang-Ba...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2014-05, Vol.47 (21), p.215201-17
Main Authors: Alam, I T, Batchelor, M T
Format: Article
Language:English
Subjects:
Boundaries
Dilution
discrete holomorphicity
Integral calculus
Invariance
Inversions
Lattices
loop models
Mathematical analysis
Mathematical models
Yang-Baxter integrability
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Summary:In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the conditions for integrability, namely, the inversion and Yang-Baxter relations, can be derived from the condition of holomorphicity of the observables. Furthermore, the Z-invariance of the models is shown to result in the invariance of the observables on the boundary of a sublattice under reshuffling of the rhombuses of its planar rhombic embedding.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/21/215201