Corner contribution to percolation cluster numbers in three dimensions

István A. Kovács; Ferenc Iglói

doi:10.1103/PhysRevB.89.174202

Corner contribution to percolation cluster numbers in three dimensions

István A. Kovács, Ferenc Iglói

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 bΓlnLΓ, with 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.

Original language	English (US)
Article number	174202
Journal	Physical Review B - Condensed Matter and Materials Physics
Volume	89
Issue number	17
DOIs	https://doi.org/10.1103/PhysRevB.89.174202
State	Published - May 12 2014

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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title = "Corner contribution to percolation cluster numbers in three dimensions",

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 bΓlnLΓ, with 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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AU - Iglói, Ferenc

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N2 - 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 bΓlnLΓ, with 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.

AB - 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 bΓlnLΓ, with 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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