Correlations of the percolation energy field and its logarithmic partner

TL;DR

This paper investigates the critical behavior of two correlated lattice fields in site percolation on a triangular lattice, demonstrating their conformal invariance and alignment with logarithmic conformal field theory predictions.

Contribution

It introduces a pair of lattice fields forming a logarithmic pair at criticality and analyzes their correlation functions, linking them to known percolation phenomena.

Findings

Correlation functions have well-defined scaling limits.

The structure matches predictions of logarithmic conformal field theory.

One field relates to the percolation energy, the other to four-arm events.

Abstract

For site percolation on the triangular lattice, we define two lattice fields that form a logarithmic pair in the sense of conformal field theory. We show that, at the critical point, their two- and three-point correlation functions have well-defined scaling limits, whose structure agrees with that predicted for logarithmic field theories. One of the two fields can be identified with the percolation analog of the Ising energy field, while the other is related to the percolation four-arm event.