Stochastic Growth in a Small World

TL;DR

This paper investigates the Edwards-Wilkinson model on small-world networks, revealing that spectral properties cause a finite surface width even with weak random interactions, through numerical analysis.

Contribution

It provides the first detailed numerical study of the spectral gap in the Edwards-Wilkinson model on small-world networks, linking spectral features to surface width behavior.

Findings

Spectral gap or pseudo-gap observed in the coupling matrix spectrum.

Finite surface width persists in the thermodynamic limit with weak randomness.

Exact numerical diagonalization confirms the spectral influence on surface roughness.

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.