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.

Figure 1

(a) Schematic phase diagram in the $\lambda -{\lambda }_1$ plane ($d<4$), showing the regions corresponding to a rough phase (stripes) and a crumpled phase (checkerboard). (b) Schematic phase diagram and the RG flow lines in the $g-\gamma$ plane ($d<4$). The small solid circle on the $g$ axis is the original LDS fixed point $g=8\epsilon /3$. The red curved line is the fixed line $g=\epsilon /\left[3\mathrm{\Delta }\right(\gamma \left)\right]$. (c) Conjectured “Occam's razor” global RG flows in the $g-\gamma$ plane ($d<4$). Arrows indicate the flow directions. The green and blue broken lines give the boundary between the stable (rough) and the crumpled phases. The small solid red square on the $g$ axis is the putative unstable fixed point not accessible in our perturbative RG (see text).

Figure 2

(a) Schematic phase diagram and the RG flow lines in the $g-\gamma$ plane ($d>4$). The red curved lines are the unstable fixed lines given by $g=\epsilon /3\left|\mathrm{\Delta }\right|,\mathrm{\Delta }<0$. The shaded region has only a smooth phase; elsewhere there is a roughening transition. (b) Conjectured “Occam's razor” global RG flows in the $g-\gamma$ plane ($d>4$). Arrows indicate the flow directions. The red curved lines are the unstable fixed lines that reduce to $g=\epsilon /3\left|\mathrm{\Delta }\right|,\mathrm{\Delta }<0$, in the lowest-order perturbation theory. (c) Phases in the $\gamma -\epsilon$ plane. Loss of order across the transitions is shown (see text).