A duality principle in spin glasses

Antonio Auffinger, Wei Kuo Chen

Research output: Contribution to journalArticlepeer-review


We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature parameter, we show that this relation is valid in a large class of disordered systems. In particular, when applied to mean field spin glasses, this duality provides an interpretation of the Parisi formula as an inverted variational principle, establishing a prediction of Guerra [13].

Original languageEnglish (US)
Article number61
JournalElectronic Journal of Probability
StatePublished - 2017


  • Large deviation
  • Legendre duality
  • Parisi formula
  • Spin glass

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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