  We revisit the problem of wavefunction statistics at the Anderson
metal-insulator transition (MIT) of non-interacting electrons in d > 2 spatial
dimensions. At the transition, the complex spatial structure of the critical
wavefunctions is reflected in the non-linear behavior of the multifractal
spectrum of generalized inverse participation ratios (IPRs). Beyond the
crossover from narrow to broad IPR statistics, which always occurs for
sufficiently large moments of the wavefunction amplitude, the spectrum obtained
from a typical wavefunction associated with a particular disorder realization
differs markedly from that obtained from the disorder-averaged IPRs. This
phenomenon is known as the termination of the multifractal spectrum. We provide
a field theoretical derivation for the termination of the typical multifractal
spectrum, by combining the non-linear sigma model framework, conventionally
used to access the MIT in d = 2 + epsilon dimensions, with a functional
renormalization group (FRG) technique. The FRG method deployed here was
originally pioneered to study the properties of the two-dimensional (2D) random
phase XY model [D. Carpentier and P. Le Doussal, Nucl. Phys. B 588, 565
(2000)]. The same method was used to demonstrate the termination of the
multifractal spectrum in the very special problem of 2D Dirac fermions subject
to a random Abelian vector potential. Our result shows that the typical
multifractal wavefunction spectrum and its termination can be obtained at a
generic Anderson localization transition in d > 2, within the standard field
theoretical framework of the non-linear sigma model, when combined with the
FRG.
