Rough or crumpled: Phases in kinetic growth with surface relaxation

We show that generic kinetic growth processes with surface relaxations can exhibit a hitherto unexplored crumpled phase with short-range orientational order at dimensions d<4. A sufficiently strong spatially nonlocal 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 nonlocal particle chemical potential. Experimental and theoretical implications of these results are discussed.