Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model

Abstract

The phase diagram of the Gross-Neveu model in $2+1$ space-time dimensions at non-zero temperature and chemical potential is studied in the limit of infinitely many flavors, focusing on the possible existence of inhomogeneous phases, where the order parameter $\sigma$ is non-uniform in space. To this end, we analyze the stability of the energetically favored homogeneous configuration $\sigma (\text{x})=\bar{\sigma }=\text{const}$ with respect to small inhomogeneous fluctuations, employing lattice field theory with two different lattice discretizations as well as a continuum approach with Pauli-Villars regularization. Within lattice field theory, we also perform a full minimization of the effective action, allowing for arbitrary 1-dimensional modulations of the order parameter. For all methods special attention is paid to the role of cutoff effects. For one of the two lattice discretizations, no inhomogeneous phase was found. For the other lattice discretization and within the continuum approach with a finite Pauli-Villars cutoff parameter $\Lambda$, we find a region in the phase diagram where an inhomogeneous order parameter is favored. This inhomogeneous region shrinks, however, when $a$ is decreased or $\Lambda$ is increased, and finally diappears for all non-zero temperatures when the cutoff is removed completely. For vanishing temperature, we find hints for a degeneracy of homogeneous and inhomogeneous solutions, in agreement with earlier findings.

37 pages, 10 figures, contains ancillary files with plot data

References in corpus (14)

• The QCD phase structure at finite temperature and density
• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Susceptibilities near the QCD (tri)critical point
• UV fixed-point structure of the three-dimensional Thirring model
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Inhomogeneous chiral condensates in three-flavor quark matter
• Phase diagram of the large $N$ Gross-Neveu model in a finite periodic box
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking
• Fermions in the pseudoparticle approach
• New baryon matter in the lattice Gross-Neveu model
• Lattice investigation of an inhomogeneous phase of the 2+1-dimensional Gross-Neveu model in the limit of infinitely many flavors

Cited by in corpus (17)

• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$. II. Nonzero temperature and chemical potential
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance
• Remnants of large-$N_{\mathrm{f}}$ inhomogeneities in the 2-flavor chiral Gross-Neveu model
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions
• Renormalizing the Quark-Meson-Diquark Model
• Dissecting the moat regime at low energies I: Renormalization and the phase structure
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
• Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation