{"id":"openai-math/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions","pdf":"https://github.com/openai/math/blob/main/preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026/bloch-law-heisenberg.pdf","url":"https://github.com/openai/math/tree/main/preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026","tags":["statistical-mechanics","heisenberg-ferromagnet","magnetization"],"score":0,"title":"Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions","domain":"Mathematical physics","family":"271","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove Bloch's T 3/2 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 ℤ 3 , 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Bloch's law, its lattice correction, and the spherical magnetization law"}