Reference request: 2D conformal field theory and the honeycomb lattice

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Would anyone know what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie the function is defined on the vertices of the dual tringular lattice)? Supposedly this falls under the purview of 2D conformal field theory but I'm finding the physics papers on the subject hard to parse.

I would appreciate a pointer to a gentle introduction to the subject, preferably in the context of statistical physics.