Corner contribution to percolation cluster numbers in three dimensions

In three-dimensional critical percolation we study numerically the number of clusters, $N_Γ$, which intersect a given subset of bonds, $Γ$. If $Γ$ represents the interface between a subsystem and the environment, then $N_Γ$ is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in $Γ$ there are singular corrections to $N_Γ$, which scale as $b_Γ \ln L_Γ$, $L_Γ$ being the linear size of $Γ$ and the prefactor, $b_Γ$, is found to be universal. This result indicates that logarithmic finite-size corrections exist in the free-energy of three-dimensional critical systems.

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