Corner contribution to percolation cluster numbers

István A. Kovács, F. Iglói, John Cardy

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number214203
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number21
DOIs
Publication statusPublished - Dec 7 2012

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Ising model
Invariance
Entropy
set theory
invariance
entropy
continuums
curves
simulation
Monte Carlo simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

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

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 86, No. 21, 214203, 07.12.2012.

Research output: Contribution to journalArticle

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