  Ever since the experiments which founded the field of highly frustrated
magnetism, the kagome Heisenberg antiferromagnet has been the archetypical
setting for the study of fluctuation induced exotic ordering. To this day the
nature of its classical low-temperature state has remained a mystery: the
non-linear nature of the fluctuations around the exponentially numerous
harmonically degenerate ground states has not permitted a controlled theory,
while its complex energy landscape has precluded numerical simulations at low
temperature. Here we present an efficient Monte Carlo algorithm which removes
the latter obstacle. Our simulations detect a low-temperature regime in which
correlations saturate at a remarkably small value. Feeding these results into
an effective model and analyzing the results in the framework of an appropriate
field theory implies the presence of long-range dipolar spin order with a
tripled unit cell.
