Three-Point Functions in the Fully Packed Loop Model on the Honeycomb Lattice. Dupic, T., Estienne, B., & Ikhlef, Y. Journal of Physics A: Mathematical and Theoretical, 52(20):205003, April, 2019.
doi  abstract   bibtex   
The fully-packed loop model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin (1991 J. Phys. A: Math. Gen. 24 2387). Using the two-component Coulomb-gas approach of Kondev et al (1996 J. Phys. A: Math. Gen. 29 6489), 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.
@article{dupicThreepointFunctionsFully2019,
  title = {Three-Point Functions in the Fully Packed Loop Model on the Honeycomb Lattice},
  author = {Dupic, T. and Estienne, B. and Ikhlef, Y.},
  year = {2019},
  month = apr,
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {52},
  number = {20},
  pages = {205003},
  issn = {1751-8121},
  doi = {10.1088/1751-8121/ab1725},
  urldate = {2019-08-08},
  abstract = {The fully-packed loop model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin (1991 J. Phys. A: Math. Gen. 24 2387). Using the two-component Coulomb-gas approach of Kondev et al (1996 J. Phys. A: Math. Gen. 29 6489), 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.},
  langid = {english},
  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/MVHCVQU6/Dupic et al. - 2019 - Three-point functions in the fully packed loop mod.pdf}
}

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