### Abstract

We study the number of clusters in two-dimensional (2d) critical percolation, N_{Γ}, which intersect a given subset of bonds, Γ. In the simplest case, when Γ is a simple closed curve, N _{Γ} is related to the entanglement entropy of the critical diluted quantum Ising model, in which Γ represents the boundary between the subsystem and the environment. Due to corners in Γ there are universal logarithmic corrections to N_{Γ}, which are calculated in the continuum limit through conformal invariance, making use of the Cardy-Peschel formula. The exact formulas are confirmed by large-scale Monte Carlo simulations. These results are extended to anisotropic percolation where they confirm a result of discrete holomorphicity.

Original language | English |
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Article number | 214203 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 86 |

Issue number | 21 |

DOIs | |

Publication status | Published - Dec 7 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*86*(21), [214203]. https://doi.org/10.1103/PhysRevB.86.214203

**Corner contribution to percolation cluster numbers.** / Kovács, István A.; Iglói, F.; Cardy, John.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 86, no. 21, 214203. https://doi.org/10.1103/PhysRevB.86.214203

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TY - JOUR

T1 - Corner contribution to percolation cluster numbers

AU - Kovács, István A.

AU - Iglói, F.

AU - Cardy, John

PY - 2012/12/7

Y1 - 2012/12/7

N2 - We study the number of clusters in two-dimensional (2d) critical percolation, NΓ, which intersect a given subset of bonds, Γ. In the simplest case, when Γ is a simple closed curve, N Γ is related to the entanglement entropy of the critical diluted quantum Ising model, in which Γ represents the boundary between the subsystem and the environment. Due to corners in Γ there are universal logarithmic corrections to NΓ, which are calculated in the continuum limit through conformal invariance, making use of the Cardy-Peschel formula. The exact formulas are confirmed by large-scale Monte Carlo simulations. These results are extended to anisotropic percolation where they confirm a result of discrete holomorphicity.

AB - We study the number of clusters in two-dimensional (2d) critical percolation, NΓ, which intersect a given subset of bonds, Γ. In the simplest case, when Γ is a simple closed curve, N Γ is related to the entanglement entropy of the critical diluted quantum Ising model, in which Γ represents the boundary between the subsystem and the environment. Due to corners in Γ there are universal logarithmic corrections to NΓ, which are calculated in the continuum limit through conformal invariance, making use of the Cardy-Peschel formula. The exact formulas are confirmed by large-scale Monte Carlo simulations. These results are extended to anisotropic percolation where they confirm a result of discrete holomorphicity.

UR - http://www.scopus.com/inward/record.url?scp=84871082252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871082252&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.86.214203

DO - 10.1103/PhysRevB.86.214203

M3 - Article

VL - 86

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 21

M1 - 214203

ER -