2001/11/30 by Jesper Lykke Jacobsen, J. L. Jacobsen, Paul Zinn-Justin +1
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Conformal map #Dimension (graph theory) #Eigenvalues and eigenvectors #Exponent #Geometry #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Monochromatic color #Optics #Percolation (cognitive psychology) #Physics #Quantum mechanics #Random Matrices and Applications #Stochastic processes and statistical mechanics #Tangent #Theoretical and Computational Physics #Topology (electrical circuits) #Transfer (computing) #Transfer matrix #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/35/9/304
published as J. Phys. A 35 (2002), 2131--2144 · 19 pages
arxiv created 2002/01/30 · openalex publication_date 2002/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D b to the highest eigenvalue of the transfer matrix T , and we obtain the result D b = 1.6431 ± 0.0006. For a strip of width L , T is roughly of size 2 3 L , but we manage to reduce it to ∼ L !. We find that the value of D b is stable with respect to inclusion of additional ‘blobs’ tangent to the backbone in a finite number of points.