Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos

Martínez, A.; Raya, Alfredo

doi:10.3390/sym11040492

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…What happens if the gap equation is allowed to iterate itself freely? We found only one, recently published, paper which asks exactly this question and comes to a clear conclusion: if the system is strongly coupled, chaos emerges and one can observe an infinite spectrum of 'unexpected' gap solutions with increasing coupling strength [14]. In the paper we present, we provide a brief explanation why these unexpected solutions actually should be expected.…”

Section: Introductionmentioning

confidence: 83%

Chaos in QCD? Gap Equations and Their Fractal Properties

2023

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In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach, gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cut-off. The transition domain between these two energy-separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, and determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition.

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Section: Introductionmentioning

confidence: 83%

Chaos in QCD? Gap Equations and Their Fractal Properties

2023

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“…What happens if the gap equation is allowed to iterate itself freely? We found only one, recently published, paper which asks exactly this question and comes to a clear conclusion: if the system is strongly coupled, chaos emerges and one can observe an infinite spectrum of 'unexpected' gap solutions with increasing coupling strength [14]. In the paper we present, we give a brief explanation why these unexpected solutions actually should be expected.…”

Section: Introductionmentioning

confidence: 85%

Chaos in QCD? Gap equations and their fractal properties

Klaehn,

Loveridge,

Cierniak

2021

Preprint

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We discuss how iterative solutions of QCD inspired gap-equations at finite chemical potential show domains of chaotic behavior as well as non-chaotic domains which represent one or the other of the only two -usually distinct -positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cutoff. The transition domain between these two energy separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition.

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“…In general the cutoff is fixed in order to fit known physical quantities. However some care must be taken since there are critical values for the set of parameters where the solution of the gap equation turns chaotic [51,52].…”

Section: Inverse Magnetic Catalysis and The Magnetized Phase Diagram ...mentioning

confidence: 99%

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: The linear sigma model with quarks and the Nambu--Jona-Lasinio model effective descriptions

Ayala,

Hernández,

Loewe

et al. 2021

Preprint

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We review the main features of the QCD phase diagram description, at finite temperature, baryon density and in the presence of a magnetic field, from the point of view of effective models, whose main ingredient is chiral symmetry. We concentrate our attention on two of these models: The linear sigma model with quarks and the Nambu-Jona-Lasinio model. We show that a main ingredient to understand the characteristics of the phase transitions is the inclusion of plasma screening effects that capture the physics of collective, long-wave modes, and thus describe a prime property of plasmas near transition lines, namely, long distance correlations. Inclusion of plasma screening makes possible to understand the inverse magnetic catalysis phenomenon even without the need to consider magnetic field-dependent coupling constants. Screening is also responsible for the emergence of a critical end point in the phase diagram even for small magnetic field strengths. Although versatile, the NJL model is also a more limited approach since, being a non-renormalizable model, a clear separation between pure vacuum and medium effects is not always possible. The model cannot describe inverse magnetic catalysis unless a magnetic field dependent coupling is included. The location of the critical end point strongly depends on the choice of the type of interaction and on the magnetic field dependence of the corresponding coupling. Overall, both models provide sensible tools to explore the properties of magnetized, strongly interacting matter. However, a cross talk among them as well as a consistent physical approach to determine the model parameters is much needed.

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Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos

Cited by 4 publications

References 18 publications

Chaos in QCD? Gap Equations and Their Fractal Properties

Chaos in QCD? Gap Equations and Their Fractal Properties

Chaos in QCD? Gap equations and their fractal properties

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: The linear sigma model with quarks and the Nambu--Jona-Lasinio model effective descriptions

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