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The Quantum-to-Classical mapping of a T=0 phase transition maps the critical
field theory of a continuous quantum phase transition onto a classical one in
higher dimensions. Recently, it has been shown, that this mapping breaks down
in the SU(N)xSU(N/2) Bose-Fermi Kondo model (BFKM) [1] and the spin-boson
model [2]. In [2], it was argued that this breakdown is associated with the
long-range nature of the interaction along imaginary time.
Starting from a path-integral over the group SU(2) we anaylze the role the
Berry phase term plays in the breakdown.
In the spin-anisotropic case, we employ a microscopic mapping [3] of the
BFKM onto a long-ranged Ising model to anaylze the critical behavior of both models.
[1] L. Zhu, S. Kirchner, Q. Si and A. George, Phys. Rev. Lett. 93, 267201 (2004) [2] M. Vojta, N-H. Tong and R. Bulla, Phys. Rev. Lett. 94, 070604 (2005). [3] S.Kirchner and Q.Si, Phys.Rev. Lett. 100, 026403 (2008). |
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