Open Access

Adrian Koenigstein, Laurin Pannullo

• We continue previous investigations of the (inhomogeneous) phase structure of the Gross-Neveu model in a noninteger number of spatial dimensions (1≤d<3) in the limit of an infinite number of fermion species (N→∞) at (non)zero chemical potential μ. In this work, we extend the analysis from zero to nonzero temperature T. The phase diagram of the Gross-Neveu model in 1≤d<3 spatial dimensions is well known under the assumption of spatially homogeneous condensation with both a symmetry broken and a symmetric phase present for all spatial dimensions. In d=1 one additionally finds an inhomogeneous phase, where the order parameter, the condensate, is varying in space. Similarly, phases of spatially varying condensates are also found in the Gross-Neveu model in d=2 and d=3, as long as the theory is not fully renormalized, i.e., in the presence of a regulator. For d=2, one observes that the inhomogeneous phase vanishes, when the regulator is properly removed (which is not possible for d=3 without introducing additional parameters). In the present work, we use the stability analysis of the symmetric phase to study the presence (for 1≤d<2) and absence (for 2≤d<3) of these inhomogeneous phases and the related moat regimes in the fully renormalized Gross-Neveu model in the μ,T-plane. We also discuss the relation between "the number of spatial dimensions" and "studying the model with a finite regulator" as well as the possible consequences for the limit d→3.