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Logarithmic observables in critical percolation · Around

2012

Logarithmic observables in critical percolation

Vasseur, Romain, Jacobsen, Jesper Lykke, Saleur, Hubert

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Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far.

Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1.
The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters.
In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly.

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