On the energy landscape of spherical spin glasses

Antonio Auffinger, Wei Kuo Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.

Original languageEnglish (US)
Pages (from-to)553-588
Number of pages36
JournalAdvances in Mathematics
StatePublished - May 25 2018


  • Energy landscapes
  • Parisi formula
  • Replica symmetry breaking
  • Spherical spin glasses

ASJC Scopus subject areas

  • Mathematics(all)

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