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 $α_k 2^{α_1+\dotsb+α_n}$ where $α_k$ 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.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 $α_k 2^{α_1+\dotsb+α_n}$ where $α_k$ 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.

arXiv:1811.10530Nov 26, 20184 citations

QUANTUM FIELD THEORY IN THE HEISENBERG PICTURE

World Scientific lecture notes in physicsNov 1, 199022 citations

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

α_k 2^{α_1+\dotsb+α_n}

where

α_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.