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We show the absence of an instability of homogeneous (chiral) condensates against spatially inhomogeneous perturbations for various 2+1-dimensional four-fermion and Yukawa models. All models are studied at non-zero baryon chemical potential, while some of them are also subjected to chiral and isospin chemical potential. The considered theories contain up to 16 Lorentz-(pseudo)scalar fermionic interaction channels. We prove the stability of homogeneous condensates by analyzing the bosonic two-point function, which can be expressed in a purely analytical form at zero temperature. Our analysis is presented in a general manner for all of the different discussed models. We argue that the absence of an inhomogeneous chiral phase (where the chiral condensate is spatially non-uniform) follows from this lack of instability. Furthermore, the existence of a moat regime, where the bosonic wave function renormalization is negative, in these models is ruled out.
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.
In this work, the phase diagram of the 2+1-dimensional Gross-Neveu model is investigated with baryon chemical potential as well as chiral chemical potential in the mean-field approximation. We study the theory using two lattice discretizations, which are both based on naive fermions. An inhomogeneous chiral phase is observed only for one of the two discretizations. Our results suggest that this phase disappears in the continuum limit.