### Description

We study the phase diagram of the Hubbard model in the limit
where U,
the onsite repulsive interaction, is much smaller than the
bandwidth. We
present an asymptotically exact expression for T$_c$, the
superconducting
transition temperature, in terms of the correlation
functions of the non-interacting
system which is valid for arbitrary densities so long as the
interactions are
sufficiently small. Our strategy for computing T$_c$
involves first integrating
out all degrees of freedom having energy higher than an
unphysical initial cutoff $\Omega_0$. Then, the
renormalization group (RG) flows of the resulting effective
action are computed and T$_c$ is obtained by determining the
scale below which the RG flows in the Cooper channel
diverge. We prove that T$_c$ is independent of $\Omega_0$.

### Primary author

Prof.
Srinivas Raghu
(Rice University/Stanford)