  From ultracold atoms to quantum chromodynamics, reliable ab initio studies of
strongly interacting fermions require numerical methods, typically in some form
of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at
finite density (spin polarization) generally have a sign problem, such that
those ab initio calculations are impractical. It is well-known, however, that
in the relativistic case imaginary chemical potentials solve this problem,
assuming the data can be analytically continued to the real axis. Is this
feasible for nonrelativistic systems? Are the interesting features of the phase
diagram accessible in this manner? By introducing complex chemical potentials,
for real total particle number and imaginary polarization, the sign problem is
avoided in the nonrelativistic case. To give a first answer to the above
questions, we perform a mean-field study of the finite-temperature phase
diagram of spin-1/2 fermions with imaginary polarization.
