The mean-field quantum Heisenberg ferromagnet via representation theory

Gil Alon, Gady Kozma

Research output: Contribution to journalArticlepeer-review


We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function αk2α1+···+αn where αk is the number of cycles of length k of a permutation. In the mean-field case, we simplify the formula further, arriving at a closed-form expression for the magnetisation, which allows to analyse the phase transition.

Original languageEnglish
Pages (from-to)1203-1228
Number of pages26
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
StatePublished - Aug 2021

Bibliographical note

Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2021.


  • Interchange process
  • Magnetisation
  • Phase transition
  • Quantum heizenberg ferromagnet
  • Random walk
  • Symmetric group


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