Existence of Two-Step Replica Symmetry Breaking for the Spherical Mixed p-Spin Glass at Zero Temperature

Antonio Auffinger*, Qiang Zeng

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations


We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is purely atomic and has exactly three distinct points in its support. We then derive a few consequences for the topology of the random landscape in these cases. Our main result also provides a negative answer to a question raised in 2011 by Auffinger and Ben Arous about the classification of pure-like and full mixture models.

Original languageEnglish (US)
Pages (from-to)377-402
Number of pages26
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 1 2019


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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