Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 271-04. Spontaneous magnetization in the quantum Heisenberg ferromagnet
Manuscript map · lines 7925–7934
OpenAI@2026-10-07#rem:oai-p-271-04
Authors: OpenAI. Family 271.
Title: Spontaneous magnetization in the quantum Heisenberg ferromagnet.
Abstract: For every dimension d ≥ 3 and every spin $S{}in{}{{}frac12,1,{}frac32,{}ldots{}}$, we prove that the nearest-neighbor isotropic quantum Heisenberg ferromagnet has a translation-invariant, spontaneously magnetized equilibrium state at every sufficiently low positive temperature. The same state satisfies the KMS condition for the zero-field dynamics and has magnetization at least $S/4$. This resolves the low-temperature ordering problem in the spontaneous-magnetization formulation.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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