Beyond dynamic scaling: rare events break universality

TL;DR

This paper explores a surface growth model with power-law distributed blob deposition, revealing how rare large events cause a breakdown of universality and standard scaling behavior.

Contribution

It introduces a model with power-law size distribution for deposition, showing continuous variation of critical exponents and the emergence of a second dynamical length scale.

Findings

Critical exponents vary with the power-law exponent τ.

Standard scale invariance breaks down for τ<3 due to a second length scale.

The model reveals a new phenomenology beyond traditional scale-invariant growth.

Abstract

Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-\tau}$. We find that the critical exponents vary continuously with $\tau$, recovering Kardar--Parisi--Zhang behavior only for $\tau \ge 3$. For $\tau<3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $\zeta$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $\xi$. The coexistence of these two relevant scales signals the breakdown of the usual Family--Vicsek scaling. These results point to a new phenomenology of surface growth beyond the standard scale-invariant paradigm.