Speaker
Giuseppe Benfatto
(Tor Vergata Univ.)
Description
In the last twenty years, many people in Rome have studied various
types of Fermion models, by applying rigorous RG techniques. One of
these people was Pierluigi Falco and the paper I will speak about,
written in collaboration with Vieri Mastropietro and myself, was
his last one.
The line of research on rigorous RG was open at the end of the 80's
by Giovanni Gallavotti, who published on JSP in 1990, in
collaboration with myself, a paper on the weakly interacting Fermi
gas in one and three dimensions.
In this talk I will give, without too many technical details, a review of the
results that have been obtained in the case of the one dimensional extended
Hubbard model (a gas of fermions of spin 1/2 on the one dimensional lattice)
at weak coupling and generic repulsive short range interaction.
These results concern the existence of the zero temperature limit
of the Grand Canonical Ensemble, the Borel summability of
perturbation theory and some universal relations satisfied by some
critical indices and certain thermodynamical quantities (all
depending on the coupling and all other details of the model).
These universal relations were conjectured many years ago in the
physical literature, but were checked only in some special solvable
spinless fermion models.
Primary author
Prof.
Giuseppe Benfatto
(Univ. Roma "Tor Vergata")
