{"id":"openai-math/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet","pdf":"https://github.com/openai/math/blob/main/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026","tags":["quantum-spin-systems","statistical-mechanics","ferromagnetism","mathematical-physics"],"score":0,"title":"Spontaneous magnetization in the quantum Heisenberg ferromagnet","domain":"Mathematical physics","family":"271","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"For every dimension d ≥ 3 and every spin $`S\\in\\{\\frac12,1,\\frac32,\\ldots\\}`$, we prove that the nearest-neighbor isotropic quantum Heisenberg ferromagnet has a translation-invariant, spontaneously magnetized equilibrium state at every sufficiently low positive temperature. The same state satisfies the KMS condition for the zero-field dynamics and has magnetization at least $`S/4`$. This resolves the low-temperature ordering problem in the spontaneous-magnetization formulation.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Bloch's law, its lattice correction, and the spherical magnetization law"}