Corner contribution to percolation cluster numbers in three dimensions

Abstract

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

6 pages, 7 figures. arXiv admin note: text overlap with arXiv:1210.4671

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Cited by in corpus (4)

• Strong Disorder RG approach - a short review of recent developments
• Entanglement of skeletal regions
• Cluster tomography in percolation
• Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit