Glassy States: The Free Ising Model on a Tree

Daniel Gandolfo, Christian Maes, Jean Ruiz, Senya Shlosman

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards–Anderson parameter, measuring the variance of the (random) magnetization obtained from drawing boundary conditions from the free state.

Original languageEnglish
Pages (from-to)227-237
Number of pages11
JournalJournal of Statistical Physics
Issue number1-6
Publication statusPublished - 1 Sep 2020


  • Edwards-Sokal representation
  • Extremal Gibbs state
  • Spin glass
  • Stable ground state configuration


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