Corner contribution to percolation cluster numbers in three dimensions

Kovács, István and Iglói, Ferenc (2014) Corner contribution to percolation cluster numbers in three dimensions. PHYSICAL REVIEW B, 89 (17). ISSN 2469-9950

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Abstract

In three-dimensional critical percolation we study numerically the number of clusters, NΓ, which intersect a given subset of bonds, Γ. If Γ represents the interface between a subsystem and the environment, then NΓ is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in Γ there are singular corrections to NΓ, which scale as bΓ ln LΓ, LΓ being the linear size of Γ and the prefactor, bΓ, 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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