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arXiv · 1901.02086

Three-point functions in the fully packed loop model on the honeycomb lattice

Thomas Dupic·Benoît Estienne·Yacine Ikhlef
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Abstract

The Fully-Packed Loop (FPL) model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin in 1991. Using the two-component Coulomb-Gas approach of Kondev, de Gier and Nienhuis (1996), we argue that the scaling limit consists of two degrees of freedom: a field governed by the imaginary Liouville action, and a free boson. We introduce a family of three-point correlation functions which probe the imaginary Liouville component, and we use transfer-matrix numerical diagonalisation to compute finite-size estimates. We obtain good agreement with our analytical predictions for the universal amplitudes and spatial dependence of these correlation functions. Finally we conjecture that this relation between non-intersecting loop models and the imaginary Liouville theory is in fact quite generic. We give numerical evidence that this relation indeed holds for various loop models.

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Thomas Dupic, Benoît Estienne, Yacine Ikhlef. 2019-01-07. Three-point functions in the fully packed loop model on the honeycomb lattice. https://doi.org/10.1088/1751-8121/ab1725

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