Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution

Statistical behavior and scaling properties of iso-height lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE${}_{\kappa }$). We present some evidence that the iso-height lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently SLE${}_{8\mathrm{/}3}$. This leads to the conclusion that all these discrete growth models fall into the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in two dimensions.