Correlations of the percolation energy field and its logarithmic partner

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.

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Journal
ArXiv.org
Published
2025-08-22
Primary Topic
Geochemistry and Geologic Mapping
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article
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Correlations of the percolation energy field and its logarithmic partner

ArXiv.org
Geochemistry and Geologic Mapping
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Correlations of the percolation energy field and its logarithmic partner

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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.

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Correlations of the percolation energy field and its logarithmic partner · ArXiv.org (2025) | TGRS Research Map | TGRS