Density of states near the Anderson transition in a space of dimensionality d=4−ε

Asymptotically accurate results have been obtained for the average Green’s function and the density of states in a Gaussian random potential for dimensionality of space d=4−ε over the entire energy region, including the vicinity of the mobility threshold. For N∼1 (N is the order of the perturbation theory) only parquet terms corresponding to higher terms in 1/ε are taken into account. For large N all powers of 1/ε are taken into account with their coefficients calculated in the main asymptotic limit in N. This calculation is performed by combining the condition of renormalization theory with the Lipatov asymptotic limit.