The SK Model Is Infinite Step Replica Symmetry Breaking at Zero Temperature

@article{Auffinger2020TheSM,
  title={The SK Model Is Infinite Step Replica Symmetry Breaking at Zero Temperature},
  author={A. Auffinger and Wei-Kuo Chen and Q. Zeng},
  journal={Communications on Pure and Applied Mathematics},
  year={2020},
  volume={73},
  pages={921-943}
}
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi’s prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero. 
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