Rough or crumpled: Phases in kinetic growth with surface relaxation

TL;DR

This paper investigates kinetic growth with surface relaxation, revealing a new crumpled phase with short-range order below four dimensions and discussing phase transitions influenced by non-local chemical potential effects.

Contribution

It introduces the existence of a crumpled phase in kinetic growth processes with surface relaxation and analyzes phase transitions related to non-local chemical potential effects.

Findings

Discovery of a crumpled phase with short-range order in dimensions less than 4.

Identification of a rough phase with long-range orientational order at d<4.

No crumpling transition in dimensions greater than 4, only a roughening transition.

Abstract

We show that generic kinetic growth processes with surface relaxations can exhibit a new crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially non-local part of the chemical potential associated with the particle current above a threshold in the system can trigger this crumpling. The system can also be in a perturbatively accessible rough phase with long range orientational order but short range positional order at $d<4$ with known scaling exponents. Intriguingly, in $d>4$ we argue that there is no crumpling transition; instead, there is a roughening transition from a smooth to a rough phase for large enough non-local particle current. Experimental and theoretical implications of these results are discussed.