  We have performed numerical simulations of dendritic growth at very low
undercoolings in two spatial dimension using a phase-field model. In this
regime of growth, the dendrites present sharp corners in the tip region while
the trailing region is parabolic, and the corresponding side-branching
structures resemble the shape of the tip. The scaling $v\rho^2\sim constant$,
where $\rho$ is the tip radius of curvature from the fitting to the parabolic
trailing region, still holds approximately. We find that the values of
$v\rho^2$ are consistent with those given by microscopic solvability theory.
The sharpness of the tip region of the dendrite can be characterized in terms
of the deviation $\lambda$ with respect to an Ivantsov parabola. We observe
that this length scales as $\lambda \sim \rho$, consistent with experimental
measurements.
