OpenAI · 271-02 · 2026-10-05 · Mathematical physics
The first lattice correction to Bloch's law
preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026
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.
We prove the first lattice correction to Bloch's law for the three-dimensional nearest-neighbor quantum Heisenberg ferromagnet at every fixed spin . The spontaneous-magnetization deficit agrees with the full ideal-magnon density up to . In addition to the leading Bloch term, this gives the correction . The magnetization is the right derivative at zero field of the thermodynamic pressure; the volume limit precedes the field derivative, and the low-temperature limit is taken last.
Preprint source and Lean scope
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A Lean scope note is stored for family 271, but it does not name this preprint. It names 271-04. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.
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.