Bloch's Law: 3D Heisenberg Ferromagnets

About this video

Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions
How does a quantum magnet lose its alignment? OpenAI's manuscript reports Bloch's low-temperature magnetization law, with its exact coefficient, for three-dimensional finite-range Heisenberg ferromagnets at every fixed positive half-integer spin. The assumptions include nonnegative symmetric couplings whose support generates the cubic lattice. This is a reported rigorous proof of an existing physical law.

Paper: Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions
github.com/openai/math/blob/main/preprints/Blochs-Law-for-Fin…

About the animation: A 320-arrow schematic spin lattice cools into alignment and warms into traveling tilt waves. The arrows have unit directions; they are classical visual symbols for a quantum system, not an exact quantum simulation. The displayed law is S-m(T) ~ C*T^(3/2) as T approaches zero. C = zeta(3/2)/(8*pi^(3/2)*sqrt(det(D))), with D = S/2 times sum_z J(z) z z^T. The thermodynamic limit precedes the positive-field limit, then the low-temperature limit. The animation's tilt parameter is not calibrated temperature or measured magnetization. A traveling alignment front and perspective camera are editorial schematic devices.

GitHub repository: github.com/openai/math
Related formalization scope: github.com/openai/math/blob/main/lean/docs/271.md
The linked family-level formalization scope documents spontaneous magnetization for nearest-neighbor models, not the exact Bloch coefficient animated here. The linked file does not certify the exact Bloch-law coefficient shown here.

Source-reported result. Selected theorem statements and scope were read; this is not an independent proof audit.

'Inflection' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
scottbuckley.com.au/library/inflection/
Licence: creativecommons.org/licenses/by/4.0/
Music edits: excerpted, crossfaded for looping, and gain adjusted.