Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

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.