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  • Letter
  • Open Access

Universal critical dynamics near the chiral phase transition and the QCD critical point

Johannes V. Roth1, Yunxin Ye2,*, Sören Schlichting2, and Lorenz von Smekal1,3

  • 1Institut für Theoretische Physik, Justus-Liebig-Universität, 35392 Giessen, Germany
  • 2Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
  • 3Helmholtz Research Academy Hesse for FAIR (HFHF), Campus Giessen, 35392 Giessen, Germany

  • *Present address: Institute for Theoretical Physics, Friedrich-Schiller-Universität Jena, Fröbelstieg 1, 07743 Jena, Germany.
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Phys. Rev. D 111, L111901 – Published 3 June, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L111901

Abstract

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study model H, the conjectured dynamic universality class of the quantum chromodynamics (QCD) critical point. We emphasize the structural similarities with model G, conjectured to be the dynamic universality class of the chiral phase transition in the limit of two massless quark flavors. Importantly, our formulation of the real-time FRG preserves all relevant symmetries throughout the FRG flow which, e.g., guarantees the nonrenormalization of the reversible mode couplings, as but one exact result. We derive nonperturbative RG flow equations for the kinetic coefficients of both, model G and H, in parallel, and discuss commonalities and differences in the resulting fixed-point structure and dynamic critical exponents, such as weak-scaling relations which hold in either case versus the characteristic strong scaling of model G which is absent in model H.

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References (53)

  1. M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Phys. Rev. Lett. 81, 4816 (1998).
  2. M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009).
  3. B. Berdnikov and K. Rajagopal, Phys. Rev. D 61, 105017 (2000).
  4. S. Mukherjee, R. Venugopalan, and Y. Yin, Phys. Rev. C 92, 034912 (2015).
  5. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
  6. K. Rajagopal and F. Wilczek, Nucl. Phys. B399, 395 (1993).
  7. D. T. Son and M. A. Stephanov, Phys. Rev. D 70, 056001 (2004).
  8. J. Berges, S. Schlichting, and D. Sexty, Nucl. Phys. B832, 228 (2010).
  9. M. Nahrgang, M. Bluhm, T. Schaefer, and S. A. Bass, Phys. Rev. D 99, 116015 (2019).
  10. D. Schweitzer, S. Schlichting, and L. von Smekal, Nucl. Phys. B960, 115165 (2020).
  11. D. Schweitzer, S. Schlichting, and L. von Smekal, Nucl. Phys. B984, 115944 (2022).
  12. T. Schaefer and V. Skokov, Phys. Rev. D 106, 014006 (2022).
  13. C. Chattopadhyay, J. Ott, T. Schaefer, and V. Skokov, Phys. Rev. D 108, 074004 (2023).
  14. L. J. Sieke, M. Harhoff, S. Schlichting, and L. von Smekal, Nucl. Phys. B1011, 116808 (2025).
  15. S. Schlichting, D. Smith, and L. von Smekal, Nucl. Phys. B950, 114868 (2020).
  16. A. Florio, E. Grossi, A. Soloviev, and D. Teaney, Phys. Rev. D 105, 054512 (2022).
  17. A. Florio, E. Grossi, and D. Teaney, Phys. Rev. D 109, 054037 (2024).
  18. C. Chattopadhyay, J. Ott, T. Schaefer, and V. V. Skokov, Phys. Rev. Lett. 133, 032301 (2024).
  19. L. Canet, H. Chate, and B. Delamotte, J. Phys. A 44, 495001 (2011).
  20. D. Mesterházy, J. H. Stockemer, L. F. Palhares, and J. Berges, Phys. Rev. B 88, 174301 (2013).
  21. D. Mesterházy, J. H. Stockemer, and Y. Tanizaki, Phys. Rev. D 92, 076001 (2015).
  22. J. V. Roth and L. von Smekal, J. High Energy Phys. 10 (2023) 065.
  23. J. V. Roth, Y. Ye, S. Schlichting, and L. von Smekal, J. High Energy Phys. 01 (2025) 118.
  24. Y.-r. Chen, Y.-y. Tan, and W.-j. Fu, arXiv:2406.00679.

  25. The generalization of the original (N=3)-component model G of Ref. [5] to arbitrary N is also known as the SSS model [26, 27].

  26. L. Sasvári, F. Schwabl, and P. Szépfalusy, Physica (Amsterdam) 81A, 108 (1975).
  27. U. C. Täuber, Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge University Press, Cambridge, England, 2014).
  28. I. Dzyaloshinskii and G. Volovick, Ann. Phys. (N.Y.) 125, 67 (1980).
  29. B. I. Halperin, P. C. Hohenberg, and E. D. Siggia, Phys. Rev. B 13, 1299 (1976).
  30. D. F. Litim, J. High Energy Phys. 11 (2001) 059.
  31. G. De Polsi, G. Hernández-Chifflet, and N. Wschebor, Phys. Rev. E 104, 064101 (2021).
  32. P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A 8, 423 (1973).
  33. C. De Dominicis, J. Phys. Colloques37, C1 (1976).
  34. H.-K. Janssen, Z. Phys. B 23, 377 (1976).
  35. U. C. Täuber and Z. Rácz, Phys. Rev. E 55, 4120 (1997).
  36. L. M. Sieberer, A. Chiocchetta, A. Gambassi, U. C. Täuber, and S. Diehl, Phys. Rev. B 92, 134307 (2015).
  37. L. Canet, J. Fluid Mech. 950, 1 (2022).
  38. C. Wetterich, Phys. Lett. B 301, 90 (1993).
  39. J. Berges and D. Mesterhazy, Nucl. Phys. B, Proc. Suppl. 228, 37 (2012).
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.111.L111901 for more details.
  41. J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep. 363, 223 (2002).
  42. D. F. Litim, Phys. Rev. D 64, 105007 (2001).
  43. D. F. Litim, Nucl. Phys. B631, 128 (2002).

  44. The dimensionless static coupling m¯2 is set to its value at the Wilson-Fisher fixed point within our truncation of the static free energy, which we obtain by solving the static sector of our flow equations. This poses no problem because the static flows are independent of the dynamics, as was explicitly shown in Ref. [23].

  45. E. D. Siggia, B. I. Halperin, and P. C. Hohenberg, Phys. Rev. B 13, 2110 (1976).
  46. L. T. Adzhemyan, A. N. Vasiliev, Y. S. Kabrits, and M. V. Kompaniets, Theor. Math. Phys. 119, 454 (1999).
  47. T. Ohta and K. Kawasaki, Prog. Theor. Phys. 55, 1384 (1976).
  48. N. Tetradis and C. Wetterich, Nucl. Phys. B422, 541 (1994).
  49. L. Canet, B. Delamotte, D. Mouhanna, and J. Vidal, Phys. Rev. D 67, 065004 (2003).
  50. K. Kawasaki, Ann. Phys. (Leipzig) 61, 1 (1970).
  51. M. Stephanov and Y. Yin, Phys. Rev. D 98, 036006 (2018).
  52. M. Pradeep, K. Rajagopal, M. Stephanov, and Y. Yin, Phys. Rev. D 106, 036017 (2022).
  53. P. Kovtun, G. D. Moore, and P. Romatschke, Phys. Rev. D 84, 025006 (2011).

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Phys. Rev. D 111, L111901– Published 3 June, 2025
  • Received 1 October 2024
  • Accepted 9 April 2025
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