Exact Multifractal Exponents for Two-Dimensional Percolation
arXiv:cond-mat/9901008 · doi:10.1103/PhysRevLett.82.3940
Abstract
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate exactly. The generalized dimensions D(n) as well as the MF function f(alpha) are derived from generalized conformal invariance, and are shown to be identical to those of the harmonic measure on 2D random walks or self-avoiding walks. An exact application to the anomalous impedance of a rough percolative electrode is given. The numerical checks are excellent. Another set of exact and universal multifractal exponents is obtained for n independent self-avoiding walks anchored at the boundary of a percolation cluster. These exponents describe the multifractal scaling behavior of the average nth moment of the probabity for a SAW to escape from the random fractal boundary of a percolation cluster in two dimensions.
5 pages, 3 figures (in colors)
References in corpus (1)
Cited by in corpus (34)
- 2D growth processes: SLE and Loewner chains
- Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
- A Guide to Stochastic Loewner Evolution and its Applications
- Conformally Invariant Fractals and Potential Theory
- Random planar curves and Schramm-Loewner evolutions
- Path Crossing Exponents and the External Perimeter in 2D Percolation
- Universal formula for the mean first passage time in planar domains
- The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect
- The Loewner equation: maps and shapes
- Conformal Random Geometry
- Critical percolation in the plane
- Harmonic Measure and Winding of Conformally Invariant Curves
- Multifractality of self-avoiding walks on percolation clusters
- Geometric structure of percolation clusters
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Harmonic Measure for Percolation and Ising Clusters Including Rare Events
- Almost sure multifractal spectrum of SLE
- Harmonic measure and winding of random conformal paths: A Coulomb gas perspective
- Asynchronously parallelised percolation on distributed machines
- Liouville Quantum Gravity and KPZ
- The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events
- Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters
- How anisotropy beats fractality in two-dimensional on-lattice DLA growth
- Fractal dimensions of the Q-state Potts model for the complete and external hulls
- The Coefficient Problem and Multifractality of Whole-Plane SLE and LLE
- Exponents for Hamiltonian paths on random bicubic maps and KPZ
- Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics
- Statistical Mechanics of Confined Polymer Networks
- Entropy production of entirely diffusional Laplacian transfer and the possible role of fragmentation of the boundaries
- The Harmonic Measure for critical Potts clusters
- Numerical studies of planar closed random walks
- Surveying Diffusion in Complex Geometries. An Essay
- Fractal depth-first search paths in statistical physics models
- Critical exponents for two-dimensional percolation