PHASE TRANSITIONS IN SCHEIDEGGER AND EDEN NETWORKS

摘要

We study multifractal scaling and phase transitions in Scheidegger and Eden networks in the plane on several lattices. The Horton constants R-B and R-L are found not to depend on the lattice. The scaling exponent alpha in the integrated area distribution function P(A > a) similar to a(-alpha) is found to be consistent with the relation alpha = 1 - log R-L/log R-B. The exponent alpha defines a phase transition point in the multifractal spectrum of the area distribution. The approach to this phase transition is slow and controlled by ln M, where M is the number of lattice points. For the Scheidegger model we are able to calculate the exact probability distribution p(a) for small areas a and thus to study the finite-size scaling. [References: 37]