Corner contribution to percolation cluster numbers

Journal article

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. © 2012 American Physical Society.

Authors: Kovacs, I; Igloi, F; Cardy, J

• Publication status: Published
• Journal: Physical Review B
• Volume: 86
• Issue: 21
• Publication date: 2012-12-07
• DOI: 10.1103/PhysRevB.86.214203
• EISSN: 1550-235X
• ISSN: 1098-0121
• Language: English