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.
|Number of pages||26|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|State||Published - Aug 2021|
Bibliographical noteFunding Information:
G. Kozma was supported by the Israel Science Foundation, by the Jesselson Foundation and by Paul and Tina Gardner.
© Association des Publications de l’Institut Henri Poincaré, 2021.
- Interchange process
- Phase transition
- Quantum heizenberg ferromagnet
- Random walk
- Symmetric group