OpenAI · 271-03 · 2026-10-05 · Mathematical physics
The spherical magnetization law for the three-dimensional quantum Heisenberg ferromagnet
preprints/The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-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 spherical magnetization law for the three-dimensional nearest-neighbor isotropic quantum Heisenberg ferromagnet at every fixed positive quantum spin and every sufficiently low fixed positive temperature. As the even periodic cubes grow, the symmetric zero-field magnetization converges in moments to a uniform direction with a deterministic positive magnitude. This magnitude equals the right derivative at zero field of the infinite-volume pressure. The law is expressed through self-adjoint linear combinations of the spin components and requires no joint measurement of noncommuting observables.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
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.