M. Krech, SHORT-TIME SCALING BEHAVIOR OF GROWING INTERFACES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(1), 1997, pp. 668-679
The short-time evolution of a growing interface is studied within the
framework of the dynamic renormalization-group approach for the Kadar-
Parisi-Zhang (KPZ) equation and for an idealized continuum model of mo
lecular-beam epitaxy. The scaling behavior of response and correlation
functions is reminiscent of the ''initial slip'' behavior found in pu
rely dissipative critical relaxation (model A) and critical relaxation
with conserved order parameter (model B), respectively. Unlike model
A the initial slip exponent for the KPZ equation can be expressed by t
he dynamical exponent z. In 1+1 dimensions, for which z is known exact
ly, the analytical theory for the KPZ equation is confirmed by a Monte
Carlo simulation of a simple ballistic deposition model. In 2+1 dimen
sions z is estimated from the short-time evolution of the correlation
function.