  We consider a two-dimensional Heisenberg antiferromagnet on a square lattice
with weakly coupled impurities, i.e. additional spins interacting with the host
magnet by a small dimensionless coupling constant g<<1. Using linear spin-wave
theory, we find that the magnetization disturbance at distance r from a single
impurity behaves as g/r for 1<<r<<1/g and as 1/(gr^3) for r>>1/g. Surprisingly
the disturbance is inversely proportional to the coupling constant! The
interaction between two impurities separated by a distance r is proportional to
g^2/r for 1<<r<<1/g and to 1/r^3 for r>>1/g. Hence at large distances, the
interaction is universal and independent of the coupling constant. We also find
that the frequency of Rabi oscillations between two impurities is proportional
to g^2 ln(gr) at 1<<r<<1/g, logarithmically enhanced compared to the spin-wave
width. This leads to a new mechanism for NMR, NQR and EPR line broadening. All
these astonishing results are due to the gapless spectrum of the magnetic
excitations in the quantum antiferromagnet.
