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 $m$ on the surface heights, and the latter by site-dependent random growth probabilities. Here we consider the limit $m \to \infty$, 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