Magnetized (
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)-dimensional Gross-Neveu model at finite density

Lenz, Julian J.; Mandl, Michael; Wipf, Andreas

doi:10.1103/physrevd.108.074508

Cited by 4 publications

(4 citation statements)

References 55 publications

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“…1 (right), where we plot the phase diagram in the (𝐿, 𝜇) plane for 𝐵 = 0. Similar to the situation at non-zero magnetic field, one thus observes multiple phase transitions which can be of first order and the same is also found for low non-zero temperatures [9]. Notice that, despite the finite spatial volume, these transitions are still proper phase transitions since we work in the large-𝑁 f limit and 𝑁 f and 𝑉 enter the path integral in an analogous way.…”

Section: Pos(lattice2023)172supporting

confidence: 75%

“…In order to address this question, we study the model on the lattice; in particular, we perform simulations, employing Neuberger's overlap Dirac operator [12], at 𝑁 f = 1 in order to deviate from the large-𝑁 f limit as much as possible. For details on our simulation setup, measured observables and scale-setting, as well as for a list of all parameter values we have performed simulations for, we refer to [9]. This reference also outlines how the complex-action problem arising in our simulations is avoided.…”

Section: Lattice Resultsmentioning

confidence: 99%

“…where 𝑉 = 𝛽𝐿 2 denotes the space-time volume, 𝛽 = 1/𝑇 is the inverse temperature and 𝐿 denotes the extent of space in each direction. This effective potential can be computed in closed form, see, e.g., [9] and its minimization allows for the study of the model's phase structure. The situation at vanishing chemical potential was treated exhaustively in [7], whereas we are concerned with non-zero 𝜇 but zero temperature here.…”

Section: The Large-𝑁 F Limitmentioning

confidence: 99%

“…It could, however, also be possible that our current approach simply does not allow for a sufficiently fine parameter scan with sufficiently high statistics to resolve these delicate features. Estimates on this are presented in [9].…”

Section: Pos(lattice2023)172mentioning

confidence: 99%

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The magnetized Gross-Neveu model at finite chemical potential

Mandl,

Lenz

2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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We study the (2+1)-dimensional Gross-Neveu model at non-zero chemical potential and subjected to a homogeneous background magnetic field. We do so both analytically, in the limit of an infinite number of fermion flavors in which mean-field approaches become exact, as well as on the lattice for a single flavor. The rich and exotic phase structure observed in the mean-field limit is found to be destroyed when strong quantum fluctuations are present in the system. Instead, in the phase of spontaneously broken chiral symmetry the magnetic field enhances this breaking for all choices of parameters. As a byproduct, we find indications for a first-order phase transition in the chemical potential for vanishing magnetic field but also provide hints that this could rather be a finite-size than a finite-flavor-number effect.

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Section: Pos(lattice2023)172supporting

confidence: 75%

Section: Lattice Resultsmentioning

confidence: 99%

Section: The Large-𝑁 F Limitmentioning

confidence: 99%

Section: Pos(lattice2023)172mentioning

confidence: 99%

See 2 more Smart Citations

The magnetized Gross-Neveu model at finite chemical potential

Mandl,

Lenz

2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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Fermions at finite density in the path integral approach

Podo,

Santoni

2024

J. High Energ. Phys.

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We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the iε term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the U(1) symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler-Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas-van Alphen effect. Finally, we consider a (generalized) Gross-Neveu model for N interacting fermions at finite density. We compute its non-perturbative effective potential in the large-N limit, and discuss the fate of the U(1) vector and $$ {\mathbb{Z}}_2^A $$ ℤ 2 A axial symmetries.

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Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions 1≤d<3 . II. Nonzero temperature and chemical potential

Koenigstein,

Pannullo

2024

Phys. Rev. D

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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 [L. Pannullo, Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions 1≤d<3, ]. 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. Published by the American Physical Society 2024

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Magnetized ( 2+1 )-dimensional Gross-Neveu model at finite density

Cited by 4 publications

References 55 publications

The magnetized Gross-Neveu model at finite chemical potential

The magnetized Gross-Neveu model at finite chemical potential

Fermions at finite density in the path integral approach

Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions 1≤d<3 . II. Nonzero temperature and chemical potential

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