Closed-form honeycomb mixed-correlation amplitudes

Derive closed-form bulk predictions for the amplitudes of the mixed honeycomb-lattice correlation functions \(C_{2,1}(r)\) and \(C_{3,1}(r)\), whose expected logarithmic asymptotics are currently assessed only through numerical fits.

Background

For the honeycomb Abelian sandpile model, the height probabilities and the leading coefficient of the minimally stable height correlator C1,1(r)C_{1,1}(r) are known analytically. The mixed correlators involving heights 2 and 3 are expected from the logarithmic conformal-field-theory description to have a leading r−4log⁡rr^{-4}\log r form.

The paper explicitly states that no closed-form honeycomb predictions are available for the corresponding amplitudes and therefore reports numerical slopes instead. An analytic derivation would complete the comparison between the honeycomb lattice correlations and the LCFT framework.

References

For the mixed correlators C_{2,1} and C_{3,1}, however, we are not aware of closed-form honeycomb predictions for the amplitudes, so our numerical analysis in that sector is limited to the functional form and fitted slopes.

— Universal correlations in the Abelian sandpile model  (2609.10352 - Liu et al., 9 Sep 2026) in Section 5.2, subsection “Two-point correlation functions”