  Using the exactly solvable Gross-Neveu model as theoretical laboratory, we
analyse in detail the relationship between a relativistic quantum field theory
at real and imaginary chemical potential. We find that one can retrieve the
full information about the phase diagram of the theory from an imaginary
chemical potential calculation. The prerequisite is to evaluate and
analytically continue the effective potential for the chiral order parameter,
rather than thermodynamic observables or phase boundaries. In the case of an
inhomogeneous phase, one needs to compute the full effective action, a
functional of the space-dependent order parameter, at imaginary chemical
potential.
