Introduction To Percolation Theory
- D. Stauffer, A. Aharony, S. Redner
- Physics
- 10 December 2018
Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…
Path Crossing Exponents and the External Perimeter in 2D Percolation
- M. Aizenman, B. Duplantier, A. Aharony
- Mathematics
- 4 January 1999
2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for traversals of annuli by $\ell$ non-overlapping paths, each on either occupied or vacant clusters, with at least one of…
Nonlinear scaling fields and corrections to scaling near criticality
- A. Aharony, M. Fisher
- Physics
- 1 April 1983
Random field effects in disordered anisotropic antiferromagnets
- S. Fishman, A. Aharony
- Physics
- 28 September 1979
A uniform magnetic field is shown to generate random local fields in uniaxially anisotropic antiferromagnets with random exchange interactions. This leads to a stronger divergence of the temperature…
Anomalous Diffusion on Percolating Clusters
- A. Aharony
- Mathematics
- 3 January 1983
Much of the recent renewed interest in percolation theory is related to the realization that percolation clusters are self-similar,1 and may thus be modeled by fractal structures.2 On a fractal…
Tricritical points in systems with random fields
- A. Aharony
- Physics
- 1 October 1978
Critical Behavior of Anisotropic Cubic Systems
- A. Aharony
- Materials Science, Mathematics
- 1 November 1973
The critical behavior in zero field above ${T}_{c}$ of ferromagnets or ferroelectrics with a Hamiltonian of cubic symmetry is studied, to order ${\ensuremath{\epsilon}}^{2}$, by exact…
Scaling at the percolation threshold above six dimensions
- A. Aharony, Y. Gefen, A. Kapitulnik
- Physics
- 11 March 1984
The fractal dimensionality of the infinite cluster at the percolation threshold for dimensionalities d>6 is shown to be D=4 (rather than the naive finite size scaling prediction D=d-2). Similarly,…
Critical Phenomena on Fractal Lattices
- Y. Gefen, B. Mandelbrot, A. Aharony
- Physics
- 15 September 1980
Renormalization-group techniques are applied to Ising-model spins placed on the sites of several self-similar fractal lattices. The resulting critical properties are shown to vary with the…
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