  In this work, inhomogeneous chiral phases are studied in a variety of
Four-Fermion and Yukawa models in $2+1$ dimensions at zero and non-zero
temperature and chemical potentials. Employing the mean-field approximation, we
do not find indications for an inhomogeneous phase in any of the studied
models. We show that the homogeneous phases are stable against inhomogeneous
perturbations. At zero temperature, full analytic results are presented.
