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Thermodynamic geometry of Nambu–Jona Lasinio model

  • P. Castorina
  • D. LanteriEmail author
  • S. Mancani
Regular Article

Abstract

The formalism of Riemannian geometry is applied to study the phase transitions in Nambu–Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The different thermodynamic geometrical behavior of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density gives some hints on the connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.

References

  1. 1.
    N. Ay, J. Jost, H. Van Le, L. Schwachhofer, Information Geometry, A Series of Modern Surveys in Mathematics, vol. 64 (Springer, Berlin, 2017)zbMATHGoogle Scholar
  2. 2.
    S. Amari, Information Geometry and Its Applications, Applied Mathematical Sciences, vol. 194 (Springer, Berlin, 2016)CrossRefGoogle Scholar
  3. 3.
    M. Suzuki, Information geometry and statistical manifold. arXiv:1410.3369
  4. 4.
    R.C. Rao, Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81–91 (1945)MathSciNetzbMATHGoogle Scholar
  5. 5.
    F. Weinhold, Metric geometry of equilibrium thermodynamics. J. Chem. Phys. 63, 2479, 2484, 2488, 2496 (1975)MathSciNetGoogle Scholar
  6. 6.
    George Ruppeiner, Thermodynamics: a Riemannian geometric model. Phys. Rev. A 20, 1608–1613 (1979)ADSCrossRefGoogle Scholar
  7. 7.
    George Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67, 605–659 (1995). [Erratum: Rev. Mod. Phys. 68, 313 (1996)]ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    George Ruppeiner, Anurag Sahay, Tapobrata Sarkar, Gautam Sengupta, Thermodynamic geometry, phase transitions, and the Widom line. Phys. Rev. E 86, 052103 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Helge-Otmar May, Peter Mausbach, Riemannian geometry study of vapor-liquid phase equilibria and supercritical behavior of the Lennard–Jones fluid. Phys. Rev. E 85, 031201 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Helge-Otmar May, Peter Mausbach, George Ruppeiner, Thermodynamic curvature for attractive and repulsive intermolecular forces. Phys. Rev. E 88, 032123 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    Anshuman Dey, Pratim Roy, Tapobrata Sarkar, Information geometry, phase transitions, and the Widom line: magnetic and liquid systems. Phys. A 392, 6341–6352 (2013)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Pankaj Chaturvedi, Anirban Das, Gautam Sengupta, Thermodynamic geometry and phase transitions of dyonic charged AdS black holes. Eur. Phys. J. C 77(2), 110 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    Anurag Sahay, Rishabh Jha, Geometry of criticality, supercriticality and Hawking–Page transitions in Gauss–Bonnet-AdS black holes. Phys. Rev. D 96(12), 126017 (2017)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    P. Castorina, M. Imbrosciano, D. Lanteri, Thermodynamic geometry of strongly interacting matter. Phys. Rev. D 98(9), 096006 (2018)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Paolo Castorina, Mauro Imbrosciano, Daniele Lanteri, Thermodynamic geometry and deconfinement temperature. Eur. Phys. J. Plus 134(4), 164 (2019)CrossRefGoogle Scholar
  16. 16.
    George Ruppeiner, Riemannian geometric approach to critical points: general theory. Phys. Rev. E 57, 5135–5145 (1998)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    B. Widom, The critical point and scaling theory. Physica 73(1), 107–118 (1974)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    George Ruppeiner, Thermodynamic curvature from the critical point to the triple point. Phys. Rev. E 86, 021130 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    H. Janyszek, R. Mrugala, Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39, 6515–6523 (1989)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    H. Janyszek, R. Mrugala, Riemannian and finslerian geometry and fluctuations of thermodynamic systems. Advances in Thermodynamics, vol. 3. Nonequilibrium Theory and Extremum Principles, pp. 159–174 (1990)Google Scholar
  21. 21.
    G. Ruppeiner, Thermodynamic curvature measures interactions. Am. J. Phys. 78, 1170 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Michele Floris, Hadron yields and the phase diagram of strongly interacting matter. Nucl. Phys. A 931, 103–112 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    S. Das, Identified particle production and freeze-out properties in heavy-ion collisions at RHIC Beam Energy Scan program (2014) [EPJ Web Conf. 90, 08007 (2015)]Google Scholar
  24. 24.
    L. Adamczyk et al., Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys. Rev. C 96(4), 044904 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Patrick Steinbrecher, The QCD crossover at zero and non-zero baryon densities from Lattice QCD. Nucl. Phys. A 982, 847–850 (2019)ADSCrossRefGoogle Scholar
  26. 26.
    A. Bazavov et al., The QCD equation of state to \({\cal{O}}(\mu _B^6)\) from lattice QCD. Phys. Rev. D 95(5), 054504 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    H. Janyszek, Riemannian geometry and stability of thermodynamical equilibrium systems. J. Phys. A Math. Gen. 23(4), 477–490 (1990)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    M.R. Ubriaco, The role of curvature in quantum statistical mechanics. J. Phys. Conf. Ser. 766, 012007 (2016)CrossRefGoogle Scholar
  29. 29.
    R. Ruppeiner, N. Dyjack, A. McAloon, J. Stoops, Solid-like features in dense vapors near the fluid critical point. J. Chem. Phys. 146, 224501 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    Behrouz Mirza, Hosein Mohammadzadeh, Ruppeiner geometry of anyon gas. Phys. Rev. E 78, 021127 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    M.R. Ubriaco, Stability and anyonic behavior of systems with m-statistics. Phys. A Stat. Mech. Appl. 392(20), 4868–4873 (2013)CrossRefGoogle Scholar
  32. 32.
    Anurag Sahay, Tapobrata Sarkar, Gautam Sengupta, On the thermodynamic geometry and critical phenomena of AdS black holes. JHEP 07, 082 (2010)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    G. Ruppeiner, P. Mausbach, H.-0. May, Thermodynamic r-diagrams reveal solid-like fluid states. Phys. Lett. A 379(7), 646–649 (2015)CrossRefGoogle Scholar
  34. 34.
    P. Zhuang, J. Hufner, S.P. Klevansky, Thermodynamics of a quark-meson plasma in the Nambu–Jona–Lasinio model. Nucl. Phys. A 576, 525–552 (1994)ADSCrossRefGoogle Scholar
  35. 35.
    T.M. Schwarz, S.P. Klevansky, G. Papp, The Phase diagram and bulk thermodynamical quantities in the NJL model at finite temperature and density. Phys. Rev. C 60, 055205 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    Michael Buballa, NJL model analysis of quark matter at large density. Phys. Rep. 407, 205–376 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    A. Barducci, R. Casalbuoni, G. Pettini, L. Ravagli, A NJL-based study of the QCD critical line. Phys. Rev. D 72, 056002 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    Yue Zhao, Lei Chang, Wei Yuan, Yu-xin Liu, Chiral susceptibility and chiral phase transition in Nambu–Jona–Lasinio model. Eur. Phys. J. C 56, 483–492 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    Aharon Casher, Chiral symmetry breaking in quark confining theories. Phys. Lett. 83B, 395–398 (1979)ADSCrossRefGoogle Scholar
  40. 40.
    Tom Banks, A. Casher, Chiral symmetry breaking in confining theories. Nucl. Phys. B 169, 103–125 (1980)ADSCrossRefGoogle Scholar
  41. 41.
    P. Cea, P. Castorina, Quark confinement and chiral symmetry breaking. Nuovo Cim. A 81, 567 (1984)ADSCrossRefGoogle Scholar
  42. 42.
    S. Digal, E. Laermann, H. Satz, Deconfinement through chiral symmetry restoration in two flavor QCD. Eur. Phys. J. C 18, 583–586 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    H.T. Ding, P. Hegde, F. Karsch, A. Lahiri, S.T. Li, S. Mukherjee, P. Petreczky, Chiral phase transition of (2+1)-flavor QCD. Nucl. Phys. A 982, 211–214 (2019)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità di CataniaCataniaItaly
  2. 2.INFN, Sezione di CataniaCataniaItaly
  3. 3.Dipartimento di FisicaUniversità di Roma “La Sapienza”RomeItaly
  4. 4.Institute of Particle and Nuclear Physics, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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