We study the low-temperature asymptotics of the free energy of the quantum Heisenberg ferromagnet, and show that it agrees to leading order with the one of an ideal Bose gas of magnons at criticality, as predicted by the spin-wave approximation. For the model in 3 (or more) dimensions, this was shown a few years ago (in joint work with Correggi and Giuliani), but the analysis is significantly more complicated in lower dimensions. In fact, the two-dimensional case is still open, but the one-dimensional case was recently settled (in joint work with Napiorkowski). We will explain the main ingredients in the proof.
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