Generic Dynamic Scaling in Kinetic Roughening

José J. Ramasco1,2, Juan M. López3 and Miguel A. Rodríguez1
1Instituto de Física de Cantabria (CSIC-UC), Av de los Castros s/n 39005 Santander, Spain
2Dpto. de Física Moderna, Universidad de Cantabria 39005 Santander, Spain
3Dipartimento di Fisica and UnitÓ INFM, UniversitÓ di Roma "La Sapienza", I-00185 Roma, Italy

(6 March 2000)

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation functions, which leads to the different anomalous forms of scaling recently observed in growth models. We derive all the existing forms of anomalous dynamic scaling from a new generic scaling ansatz. The different scaling forms are subclasses of this generic scaling ansatz associated with bounds on the roughness exponent values. The existence of a new class of anomalous dynamic scaling is predicted and compared with simulations.