Strong coupling phases of conserved growth models are crumpled

Abstract: We show that stochastically driven nonequilibrium conserved growth models admit strong coupling phases for sufficiently strong nonlocal chemical potentials underlying the dynamics. The models exhibit generic roughening transitions between perturbatively accessible weak coupling phases satisfying an exact relation between the dynamic $z$ and roughness $\chi$ exponents in all dimensions $d$ and strong coupling phases. In dimensions below the critical dimension, the latter phases are unstable and argued to be crumpled, and thus distinct from the well-known strong coupling rough phase of the Kardar-Parisi-Zhang equation in dimensions $d\geq 2$. At the critical dimension, conventional spatio-temporal scaling in the weak coupling phase is logarithmically modulated and are exactly obtained. These results obtained by employing a combination of nonperturbative arguments and perturbative theories, corroborated by numerical results.