Density of States near the Anderson Transition in a Four-dimensional Space. Renormalizable Models

TL;DR

This paper derives asymptotically exact results for the density of states near the Anderson transition in four-dimensional disordered systems using renormalizable models, highlighting the shift of the phase transition point in the complex plane.

Contribution

It introduces a method to calculate the density of states for renormalizable models near the Anderson transition, extending previous lattice model results with new analytical techniques.

Findings

Phase transition point shifts in the complex plane.

Regularity of the density of states for all energies.

Effective interaction remains weak despite complex plane shift.

Abstract

Asymptotically exact results are obtained for the average Green function and density of states of a disordered system for a renormalizable class of models (as opposed to the lattice models examined previously [Zh. Eksp. Teor. Fiz. 106 (1994) 560-584]). For N\sim 1 (where N is an order of the perturbation theory), only the parquet terms corresponding to the highest powers of large logarithms are retained. For large N, this approximation is inadequate because of the fast growth with N of the coefficients for the lower powers of the logarithms. The latter coefficients are calculated in the leading order in N from the Callan-Symanzik equation with results of the Lipatov method using as boundary conditions. For calculating the self-energy at finite momentum, a modification of the parquet approximation is used, that allows the calculations to be done in an arbitrary finite logarithmic approximation but in the leading order in N. It is shown that the phase transition point shifts in the complex plane, thereby insuring regularity of the density of states for all energies. The "spurious" pole is avoided in such a way that effective interaction remains logarithmically weak.