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Asymptotic Freedom in Quantum Antiferromagnet TlCuCl3

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.