  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 $\alpha_k 2^{\alpha_1+\dotsb+\alpha_n}$ 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.
