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arXiv · 1811.10530

The mean-field quantum Heisenberg ferromagnet via representation theory

Gil Alon·Gady Kozma
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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 $\alpha_k 2^{\alpha_1+\dotsb+\alpha_n}$ 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.

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Gil Alon, Gady Kozma. 2018-11-26. The mean-field quantum Heisenberg ferromagnet via representation theory. https://arxiv.org/abs/1811.10530

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