  We investigate dendritic sidebranching during crystal growth in an
undercooled melt by simulation of a phase-field model which incorporates
thermal noise of microscopic origin. As a non-trivial quantitative test of this
model, we first show that the simulated fluctuation spectrum of a
one-dimensional interface in thermal equilibrium agrees with the exact
sharp-interface spectrum up to an irrelevant short-wavelength cutoff comparable
to the interface thickness. Simulations of dendritic growth are then carried
out in two dimensions to compute sidebranching characteristics
(root-mean-square amplitude and mean spacing between sidebranches) as a
function of distance behind the tip. These quantities are found to be in good
overall quantitative agreement with the predictions of the existing linear WKB
theory of noise amplification. The extension of this study to three dimensions
remains needed to determine the origin of noise in experiments.
