Renormalization-group theory for the commutative model of tunneling states in metallic glasses

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Abstract
Using the multiplicative renormalization technique, we obtain the scaling behavior of a model for tunneling states interacting with conduction electrons in which the conduction-electron-assisted tunneling is not taken into account. There is a crossover temperature which characterizes the transition from the high-temperature region where the many-body effects are effective to a region where the dynamics is frozen in. This crossover temperature is given as an effective level splitting which is reduced from its bare value due to the interaction. The renormalized coupling constants do not scale into a strong-coupling regime. Implications for the electrical resistivity are discussed, and the conclusion is drawn that if there is any logarithmic temperature-dependent term at all, the amplitude is so small that it is very unlikely to be observable.