Multifractality in a broad class of disordered systems

Details Multifractality in a broad class of disordered systems Multifractality in a broad class of disordered systems

2004-09-21

arxiv.org/abs/cond-mat/0409535v1

Phys. Rev. E 70, 015101(R) (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevE.70.015101

We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.

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