Migdal-Kadanoff fixed point of the graded nonlinearσmodel for disordered single-particle systems without time-reversal symmetry

Abstract

The critical behavior of disordered single-particle systems without time-reversal symmetry is described by a nonlinear σ model defined over a graded pseudounitary coset space. With use of the Migdal-Kadanoff approximate renormalization group relations, the fixed point of this model is studied for d=2+ε and d=3 dimensions. It is found that the properties of the fixed point for d=3 are dominated by the noncompact degrees of freedom of the model. The critical exponent ν for d=3 satisfies the inequality recently derived by Chayes et al.