Strong Coupling in Conserved Surface Roughening: A New Universality Class?
Résumé
The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (CKPZ) is thought to set the universality class instead. This has non-mean-field behavior only in spatial dimension d < 2. We point out here that CKPZ is incomplete: It omits a symmetry-allowed nonlinear gradient term of the same order as the one retained. Adding this term, we find a parameter regime where the one-loop renormalization group flow diverges. This suggests a phase transition to a new growth phase, possibly ruled by a strongcoupling fixed point and thus described by a new universality class, for any d > 1. In this phase, numerical
integration of the model in d = 2 gives clear evidence of non-mean-field behavior.
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