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PreprintCC BY 4.0arXiv

The QCD phase diagram and critical end point at finite magnetic field from holography with neural networks

  • Shaojie Liu
  • Yehong Zhang
  • Hui Liu
  • Xuanmin Cao
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Abstract

We study the magnetic-field-driven critical end point (CEP) of the QCD thermal transition at zero baryon chemical potential using a five-dimensional Einstein--Maxwell--dilaton (EMD) model. We calibrate the model to lattice entropy at zero and finite magnetic fields using a neural-network formulation of holographic radial evolution. As the magnetic field increases, the thermal transition changes from a crossover to a first-order transition. The merger of temperature turning points, a divergent specific heat, and a vanishing squared sound speed identify (eBc,Tc)≃(7.22 GeV2,95.9 MeV). The transition-region inflection of s/T3 defines the crossover temperature, while an equal-pressure Maxwell construction determines the first-order coexistence line. The two lines meet at the CEP. The change of transition order agrees qualitatively with lattice results. The phase boundary is a prediction of the calibrated model.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026phase,
  title = {{The QCD phase diagram and critical end point at finite magnetic field from holography with neural networks}},
  author = {Shaojie Liu and Yehong Zhang and Hui Liu and Xuanmin Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07353},
  eprint = {2610.07353},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07353},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The QCD phase diagram and critical end point at finite magnetic field from holography with neural networks
AU  - Shaojie Liu
AU  - Yehong Zhang
AU  - Hui Liu
AU  - Xuanmin Cao
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07353
UR  - https://arxiv.org/abs/2610.07353
AB  - We study the magnetic-field-driven critical end point (CEP) of the QCD thermal transition at zero baryon chemical potential using a five-dimensional Einstein--Maxwell--dilaton (EMD) model. We calibrate the model to lattice entropy at zero and finite magnetic fields using a neural-network formulation of holographic radial evolution. As the magnetic field increases, the thermal transition changes from a crossover to a first-order transition. The merger of temperature turning points, a divergent specific heat, and a vanishing squared sound speed identify (eB_c,T_c)≃(7.22 GeV^2,95.9 MeV). The transition-region inflection of s/T^3 defines the crossover temperature, while an equal-pressure Maxwell construction determines the first-order coexistence line. The two lines meet at the CEP. The change of transition order agrees qualitatively with lattice results. The phase boundary is a prediction of the calibrated model.
ER  -