Belitz D, Kirkpatrick T R, Rollbühler Jörg
Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA.
Phys Rev Lett. 2004 Oct 8;93(15):155701. doi: 10.1103/PhysRevLett.93.155701. Epub 2004 Oct 4.
It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a nonrenormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.
结果表明，量子临界点处多个时间尺度的存在会导致临界指数的圈展开式失效，因为展开式中的系数会发散。因此，从有限阶微扰重整化群处理中得到的结果在任何意义上都可能不是对真实渐近临界行为的近似。这个问题表现为一种不可重整化的场论，或者等效地，表现为存在一个危险的无关变量。无序金属中的量子铁磁转变就是一个例子。
