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Inhomogeneous phases near the chiral critical point in NJL-type models
High Energy Physics - Phenomenology · Submitted 26 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet.
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The abstract, sentence by sentence
In this talk we discuss the role of inhomogeneous phases in the phase diagram of the Nambu-Jona-Lasinio (NJL) and the quark meson (QM) model. By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet. This picture is confirmed by a mean-field calculation for inhomogeneous phases with a one-dimensional modulation. For the latter it is shown that recent results within lower dimensional models can be extended to 3+1 dimensions. Also the respective phase diagram for the QM model is presented.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this talk we discuss the role of inhomogeneous phases in the phase diagram of the Nambu-Jona-Lasinio (NJL) and the quark meson (QM) model. | contribution 0.55 | 0.49 | 0.04 | unclear 0.83 |
| s1 | By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet. | result 0.93 | 0.83 | 0.82 | asserted 0.99 |
| s2 | This picture is confirmed by a mean-field calculation for inhomogeneous phases with a one-dimensional modulation. | result 0.91 | 0.84 | 0.13 | asserted 1.00 |
| s3 | For the latter it is shown that recent results within lower dimensional models can be extended to 3+1 dimensions. | result 0.85 | 0.68 | 0.05 | asserted 1.00 |
| s4 | Also the respective phase diagram for the QM model is presented. | contribution 0.80 | 0.77 | 0.04 | asserted 0.88 |
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The paper
Original abstract
In this talk we discuss the role of inhomogeneous phases in the phase diagram of the Nambu-Jona-Lasinio (NJL) and the quark meson (QM) model. By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet. This picture is confirmed by a mean-field calculation for inhomogeneous phases with a one-dimensional modulation. For the latter it is shown that recent results within lower dimensional models can be extended to 3+1 dimensions. Also the respective phase diagram for the QM model is presented.
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What it cites · 12 sentences without a confident label
Uses the method or tool of 4 papers
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Following Ref. [ref] we first address inhomogeneous phases by means of a generalized GL expansion, i.e. by an expansion of the thermodynamic potential as an effective action in the order parameters as well as in gradients acting on the order parameter.
How many phases meet at the chiral critical point? · Introduction and summary · 0.99
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First, we use the conserved momentum $p_⊥$ in the perpendicular x- and y-direction combined with Lorentz symmetry and express all eigenvalues through the set ${λ}$ at $p_⊥=0$ (see Ref. [ref] for details), giving [equation] Second, we observe that the Hamiltonian $H_MF$ for the case $p_⊥=0$ can be cast into the form [equation] where $H_MF;1D$ is the Hamiltonian of the GN model for the same order parameter $M(z)$.
Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model · Phase diagrams allowing for inhomogeneous ground states with a one-dimensional modulation · 0.89
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Instead of a proper renormalization we will however follow Refs. [ref] , where it has been assumed that the zero temperature contribution can well be approximated by $1/V∫_V U(σ(x),π^a(x))$ with the parameters directly adopted to phenomenology.
Susceptibilities near the QCD (tri)critical point · Inhomogeneous phases in the QM model · 0.99
Compares with 3 papers
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It is also worth noting that the GL functional takes a similar form as in the one-dimensional GN model [ref] .
Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors · Generalized Ginzburg-Landau expansion · 0.91
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It is also worth noting that the GL functional takes a similar form as in the one-dimensional GN model [ref] .
From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram · Generalized Ginzburg-Landau expansion · 0.91
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This is not the case in superconductors [ref] where the underlying dynamics is different, namely coming from particle-particle and hole-hole scattering near the Fermi surface instead of particle-hole scattering in presented case.
Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors · Generalized Ginzburg-Landau expansion · 0.92
Cites as background 14 papers
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For this model inhomogeneous phases have been investigated for the large $N$ limit [ref] , which technically corresponds to a mean-field approximation, and basically all ground-states have been classified at least for the chiral limit [ref] .
Full Phase Diagram of the Massive Gross-Neveu Model · Introduction and summary · 0.86
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For this model inhomogeneous phases have been investigated for the large $N$ limit [ref] , which technically corresponds to a mean-field approximation, and basically all ground-states have been classified at least for the chiral limit [ref] .
From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram · Introduction and summary · 0.86
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For this model inhomogeneous phases have been investigated for the large $N$ limit [ref] , which technically corresponds to a mean-field approximation, and basically all ground-states have been classified at least for the chiral limit [ref] .
Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems · Introduction and summary · 0.86
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