{"id":"openai-math/The-first-lattice-correction-to-Blochs-law","pdf":"https://github.com/openai/math/blob/main/preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026/first-lattice-correction-bloch-law.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026","tags":["condensed-matter","quantum-magnetism","heisenberg-model","statistical-mechanics"],"score":0,"title":"The first lattice correction to Bloch's law","domain":"Mathematical physics","family":"271","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove the first lattice correction to Bloch's law for the three-dimensional nearest-neighbor quantum Heisenberg ferromagnet at every fixed spin $`S=\\tfrac12,1,\\tfrac32,\\ldots`$. The spontaneous-magnetization deficit agrees with the full ideal-magnon density up to $`o(\\beta^{-5/2})`$. In addition to the leading Bloch term, this gives the correction $`3\\zeta(5/2)(\\beta S)^{-5/2}/(128\\pi^{3/2})`$. The magnetization is the right derivative at zero field of the thermodynamic pressure; the volume limit precedes the field derivative, 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"}