 95426 Joel Feldman, Manfred Salmhofer, Eugene Trubowitz
 Perturbation Theory around NonNested Fermi Surfaces
I. Keeping the Fermi Surface Fixed
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Sep 15, 95

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Abstract. The perturbation expansion for a general class of
manyfermion systems with a nonnested, nonspherical Fermi
surface is renormalized to all orders. In the limit as the
infrared cutoff is removed, the counterterms converge to a
finite limit which is differentiable in the band structure.
The map from the renormalized to the bare band structure
is shown to be locally injective. A new classification of graphs
as overlapping or nonoverlapping is given, and improved power
counting bounds are derived from it. They imply that the only
subgraphs that can generate $r$ factorials in the $r^{\rm th}$ order
of the renormalized perturbation series are indeed the ladder graphs
and thus give a precise sense to the statement that
`ladders are the most divergent diagrams'. Our results apply directly
to the Hubbard model at any filling except for halffilling.
The halffilled Hubbard model is treated in another place.
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