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

Understand

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.