Stochastic Growth in a Small World

Abstract

We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum exhibits a gap or a pseudo-gap, which is responsible for a finite width in the thermodynamic limit for an arbitrarily weak but nonzero magnitude of the random interactions.

16th Annual Workshop: Recent Developments in Computer Simulation Studies in Condensed Matter Physics, University of Georgia, GA (February 27, 2003)