OpenAI · 271-01 · 2026-10-05 · Mathematical physics
Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions
preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-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 Bloch's T3/2 law for the spontaneous magnetization of three-dimensional quantum Heisenberg ferromagnets at every fixed positive quantum spin. The result holds for every nonnegative symmetric finite-range interaction whose support generates ℤ3, including spatially anisotropic couplings. The leading magnetization deficit has the exact coefficient determined by the determinant of the quadratic one-magnon dispersion. The thermodynamic limit is taken before the right field derivative at zero, and the low-temperature limit is taken last.
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.