The mean-field quantum Heisenberg ferromagnet via representation theory

Abstract

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 ${\alpha }_k{2}^{{\alpha }_1+\cdots +{\alpha }_n}$ where ${\alpha }_k$ 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.

30 pages