Corner contribution to percolation cluster numbers

István A. Kovács*, Ferenc Iglói, John Cardy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 (US)
Article number214203
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number21
DOIs
StatePublished - Dec 7 2012

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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