  Phase transitions in isotropic quantum antiferromagnets are described by an
O(3) nonlinear quantum field theory. In three dimensions, the fundamental
property of this theory is logarithmic scaling of the coupling constant. At the
quantum critical point the coupling asymptotically vanishes and the
quasiparticles become free. This logarithmic decay of the coupling constant has
never been ob- served. In this paper, we derive finite temperature properties
of the field theory and use our results to analyze the existing data on the
real antiferromagnet TlCuCl3. Including finite temperatures into the theory, we
find that agreement between theory and experiment is sufficiently sensitive to
unambiguously identify the asymptotic decay of the coupling constant. We also
comment on the unique possibility to study Landau pole-physics in quantum
magnets.
