OpenAI · 271-04 · 2026-09-24 · Mathematical physics
Spontaneous magnetization in the quantum Heisenberg ferromagnet
preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026
Family 271. Bloch's law and spontaneous ferromagnetic order.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Time. A clock or ferromagnet statement is not quantum evolution without an external time. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Em02-E · VI
Proves Bloch's law with its exact coefficient for three-dimensional quantum Heisenberg ferromagnets at every positive quantum spin, allowing nonnegative symmetric finite-range couplings whose support generates . The thermodynamic limit precedes the zero-field derivative and low-temperature limit. The family also proves spontaneous magnetization for nearest-neighbor models in every dimension and determines the first lattice correction for three-dimensional nearest-neighbor couplings.
For every dimension d ≥ 3 and every spin , 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 . This resolves the low-temperature ordering problem in the spontaneous-magnetization formulation.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 271: Bloch's law, its lattice correction, and the spherical magnetization law. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
Heisenberg.lean · Heisenberg.lean
Time
Bloch's law is not the relational clock
Family 271 records Bloch's law for the quantum Heisenberg ferromagnet. That statement is not quantum evolution without an external time and not a premise of the relational clock sheets. The authors are OpenAI. The companion does not verify those proofs.