162 research outputs found
Scaling in a simple model for surface growth in a random medium
Surface growth in random media is usually governed by both the surface
tension and the random local forces. Simulations on lattices mimic the former
by imposing a maximum gradient on the surface heights, and the latter by
site-dependent random growth probabilities. Here we consider the limit , where the surface grows at the site with minimal random number, {\it
independent} of its neighbors. The resulting height distribution obeys a simple
scaling law, which is destroyed when local surface tension is included. Our
model is equivalent to Yee's simplification of the Bak-Sneppen model for the
extinction of biological species, where the height represents the number of
times a biological species is exchanged.Comment: 11 pages including numerous figures; for Int. J. Mod. Phys.
50 years of correlations with Michael Fisher and the renormalization group
This paper will be published in ``50 years of the renormalization group",
dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora
Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific. I start with
a review of my personal and scientific interactions with Michael E. Fisher, who
was my post-doc mentor in 1972-1974. I then describe several recent
renormalization group studies, which started during those years, and still
raise some open issues. These include the magnets with dipole-dipole
interactions, the puzzle of the bicritical points and the random field Ising
model.Comment: Added Fig. 4 ad foototes. Pls identify people in Fig
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