On properties of the spherical mixed vector p-spin model

Antonio Auffinger*, Yuxin Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti–Sommers formula recently obtained in Ko (2018). In particular, we extend some of the one-dimensional Parisi measure results of Auffinger and Chen (2015) to the vector case.

Original languageEnglish (US)
Pages (from-to)382-413
Number of pages32
JournalStochastic Processes and their Applications
StatePublished - Apr 2022


  • Crisanti–Sommers
  • Ground state energy
  • Parisi's formula
  • Spherical vector p-spin
  • Spin glass

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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