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

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

We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different...

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Bibliographic Details
Main Authors: Angelo Martínez, Alfredo Raya
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Symmetry
Subjects:
Nambu-Jona-Lasinio model
superstrong coupling
magnetic field
heat bath
Online Access:https://www.mdpi.com/2073-8994/11/4/492
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spelling doaj-16669ab54b6e45348818e0e28160636f2020-11-25T02:18:26ZengMDPI AGSymmetry2073-89942019-04-0111449210.3390/sym11040492sym11040492Solving the Gap Equation of the NJL Model through Iterations: Unexpected ChaosAngelo Martínez0Alfredo Raya1Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, Francisco J. Múgica s/n, Col. Felícitas del Río, Morelia 58040, Michoacan, MexicoInstituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, Francisco J. Múgica s/n, Col. Felícitas del Río, Morelia 58040, Michoacan, MexicoWe explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer.https://www.mdpi.com/2073-8994/11/4/492Nambu-Jona-Lasinio modelsuperstrong couplingmagnetic fieldheat bath
collection DOAJ
language English
format Article
sources DOAJ
author Angelo Martínez
Alfredo Raya
spellingShingle Angelo Martínez
Alfredo Raya
Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
Symmetry
Nambu-Jona-Lasinio model
superstrong coupling
magnetic field
heat bath
author_facet Angelo Martínez
Alfredo Raya
author_sort Angelo Martínez
title Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
title_short Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
title_full Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
title_fullStr Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
title_full_unstemmed Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos
title_sort solving the gap equation of the njl model through iterations: unexpected chaos
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-04-01
description We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer.
topic Nambu-Jona-Lasinio model
superstrong coupling
magnetic field
heat bath
url https://www.mdpi.com/2073-8994/11/4/492
work_keys_str_mv AT angelomartinez solvingthegapequationofthenjlmodelthroughiterationsunexpectedchaos
AT alfredoraya solvingthegapequationofthenjlmodelthroughiterationsunexpectedchaos
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