Functional renormalization group study of the three-dimensional Hubbard model*

We present the extension of the truncated unity functional renormalization
group (TUfRG) approach to three-dimensional lattice models for interacting
fermions. This provides a flexible method for detecting ordering tendencies
which treats all fluctuation channels on equal footing.

As a first example, we study the Hubbard model on the simple cubic lattice.
We determine the leading ordering tendencies for low temperatures and the
corresponding energy scales for ordering. At half filling and for repulsive
interaction, the transition scale to an antiferromagnetic (AFM) ground state
shows good agreement with other numerical methods. In addition, we
investigate the competition between AFM and d-wave superconducting
ordering away from half filling.