  We study attractively interacting fermions on a square lattice with
dispersion relations exhibiting strong spin-dependent anisotropy. The resulting
Fermi surface mismatch suppresses the s-wave BCS-type instability, clearing the
way for unconventional types of order. Unbiased sampling of the Feynman
diagrammatic series using Diagrammatic Monte Carlo methods reveals a rich phase
diagram in the regime of intermediate coupling strength. Instead of a proposed
Cooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev.
Lett. 103, 025303 (2009)] we find an incommensurate density wave at strong
anisotropy and two different p-wave superfluid states with unconventional
symmetry at intermediate anisotropy.
