  Kinetics of separation between the low and high density phases in a single
component Lennard-Jones model has been studied via molecular dynamics
simulations, at a very low temperature, in the space dimension $d=2$. For
densities close to the vapor (low density) branch of the coexistence curve,
disconnected clusters of the high density phase exhibit ballistic motion, the
kinetic energy distribution of the clusters being closely Maxwellian. Starting
from nearly circular shapes, at the time of nucleation, these clusters grow via
sticky collisions, gaining filament-like nonequilibrium structure at late
times, with a very low fractal dimensionality. The origin of the latter is
shown to lie in the low mobility of the constituent particles, in the
corresponding cluster reference frame, due to the (quasi-long-range)
crystalline order. Standard self-similarity in the domain pattern, typically
observed in kinetics of phase transitions, is found to be absent in this growth
process. This invalidates the common method, that provides a growth law same as
in immiscible solid mixtures, of quantifying growth. An appropriate alternative
approach, involving the fractality in the structure, quantifies the growth of
the characteristic "length" to be a power-law with time, the exponent being
surprisingly high. The observed growth law has been derived via a
nonequilibrium kinetic theory.
