2,051 research outputs found
Universality of the Directed Polymer Model
The universality of the directed polymer model and the analogous
KPZ equation is supported by numerical simulations using non-Gaussian random
probability distributions in two, three and four dimensions.
It is shown that although in the non-Gaussian cases the \emph{finite size}
estimates of the energy exponents are below the persumed universal values,
these estimates \emph{increase} with the system size, and the further they are
below the universal values, the higher is their rate of increase. The results
are explained in terms of the efficiency of variance reduction during the
optimization process.Comment: RevTeX, 3 postscript figure
Distribution of Dangling Ends on the Incipient Percolation Cluster
We study numerically and by scaling arguments the probability P(M)dM that a
given dangling end of the incipient percolation cluster has a mass between M
and M + dM. We find by scaling arguments that P(M) decays with a power law,
P(M)~M^(-(1+k)), with an exponent k=dBf/df, where df and dBf are the fractal
dimensions of the cluster and its backbone, respectively. Our numerical results
yield k=0.83 in d=2 and k=0.74 in d=3 in very good agreement with theory.Comment: proceedings of the conference "Percolation and Disordered Systems:
*Theory and Applications*", Giessen (Germany) 1998, see
http://ory.ph.biu.ac.il/PERCOLATION98/ , 4 pages, 3 figures, in press, will
be published in Physica
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