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PreprintCC BY 4.0arXiv

Asymmetric phase transitions in random noncommutative geometries

  • Benedek Bukor
  • Masoud Khalkhali
  • Samuel Kováčik
  • Adam Kubiś
  • Katarína Magdolenová
  • Nathan Pagliaroli
  • Juraj Tekel
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Abstract

In this paper, we study the asymmetric phases of the quartic type (0, 1) and (1, 0) Dirac en- sembles via three approaches: the Riemann-Hilbert approach, bootstrapping with positivity, and Hamiltonian Monte Carlo (HMC) simulations. The focus of this work is on asymmetric solutions to the Schwinger-Dyson and saddle point equations of these models, whose solution spaces prove deeply intricate. Via the Riemann-Hilbert approach, we are able to give explicit formulae for the eigenvalue distributions and free energy of various solutions. Using Hamiltonian Monte Carlo simulations, we are able to reconstruct the phase structure. Lastly, using bootstrapping with positivity, we are able to reconstruct the eigenvalue distribution of these models from their bootstrapped moments. All three methods show excellent agreement for a large matrix size.

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Cite

BibTeXRIS
BibTeX
@misc{bukor2026asymmetric,
  title = {{Asymmetric phase transitions in random noncommutative geometries}},
  author = {Benedek Bukor and Masoud Khalkhali and Samuel Kováčik and Adam Kubiś and Katarína Magdolenová and Nathan Pagliaroli and Juraj Tekel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19898},
  eprint = {2609.19898},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19898},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Asymmetric phase transitions in random noncommutative geometries
AU  - Benedek Bukor
AU  - Masoud Khalkhali
AU  - Samuel Kováčik
AU  - Adam Kubiś
AU  - Katarína Magdolenová
AU  - Nathan Pagliaroli
AU  - Juraj Tekel
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19898
UR  - https://arxiv.org/abs/2609.19898
AB  - In this paper, we study the asymmetric phases of the quartic type (0, 1) and (1, 0) Dirac en- sembles via three approaches: the Riemann-Hilbert approach, bootstrapping with positivity, and Hamiltonian Monte Carlo (HMC) simulations. The focus of this work is on asymmetric solutions to the Schwinger-Dyson and saddle point equations of these models, whose solution spaces prove deeply intricate. Via the Riemann-Hilbert approach, we are able to give explicit formulae for the eigenvalue distributions and free energy of various solutions. Using Hamiltonian Monte Carlo simulations, we are able to reconstruct the phase structure. Lastly, using bootstrapping with positivity, we are able to reconstruct the eigenvalue distribution of these models from their bootstrapped moments. All three methods show excellent agreement for a large matrix size.
ER  -