Critical site percolation on the triangular lattice: from integrability to conformal partition functions

Abstract Critical site percolation on the triangular lattice is described by Yang–Baxter solvable dilute A 2 ( stretchy="false">) loop model with crossing parameter specialized to $\lambda = \tfrac{\pi}{3}$?> λ = π 3 , corresponding contractible fugacity $\beta -2\cos 4\lambda 1$?> β − cos 4 1 . We study functional relations satisfied commuting transfer matrices of this and associated Bethe ansatz equations. The single double row are respectively endowed strip periodic boundary conditions, elements ordinary Temperley–Lieb algebras. standard modules for these algebras labelled number defects d and, in latter case, also twist $\mathsf{e}^{\mathrm{i}\gamma}$?> e mathvariant="normal">i γ Nonlinear integral equation techniques used analytically solve equations scaling limit central charge c 0 conformal weights $\Delta, \bar \Delta$?> mathvariant="normal">Δ , ˉ For ground states, we find $\Delta \Delta_{1,d+1}$?> d + conditions $(\Delta,\bar\Delta) (\Delta_{\gamma/\pi,d/2},\Delta_{\gamma/\pi,-d/2})$?> / where $\Delta_{r,s} \frac1{24}\big((3r-2s)^2-1\big)$?> r s 24 maxsize="1.2em" minsize="1.2em">( minsize="1.2em">) give explicit conjectures trace matrix each module. $d\leqslant 8$?> ⩽ 8 supported numerical solutions logarithmic form leading 20 or more eigenenergies. With conjectures, apply Markov traces obtain partition functions cylinder torus. These precisely coincide our previous results critical bond square lattice, dense $A_1^{(1)}$?> concurrence all data provides compelling evidence supporting a strong universality between two stochastic models as field theories.