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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.
We explore the phase structure of the 1+1 dimensional Gross-Neveu model at finite number of fermion flavors using lattice field theory. Besides a chirally symmetric phase and a homogeneously broken phase we find evidence for the existence of an inhomogeneous phase, where the condensate is a spatially oscillating function. Our numerical results include a crude μ-T phase diagram.
We study the μ-μ45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where μ denotes the ordinary chemical potential, μ45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.
We study the μ-μ45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where μ denotes the ordinary chemical potential, μ45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.