Proves Bloch's T3/2 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 ℤ3. 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 d ≥ 3 and determines the first lattice correction for three-dimensional nearest-neighbor couplings. (Lean)
Manuscripts (4)
Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions
October 5, 2026 · source · cite as \cite{OAI:Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026}
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.
The first lattice correction to Bloch's law
October 5, 2026 · source · cite as \cite{OAI:The-first-lattice-correction-to-Blochs-law-October-5-2026}
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.
The spherical magnetization law for the three-dimensional quantum Heisenberg ferromagnet
October 5, 2026 · source · cite as \cite{OAI:The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026}
We prove the spherical magnetization law for the three-dimensional nearest-neighbor isotropic quantum Heisenberg ferromagnet at every fixed positive quantum spin and every sufficiently low fixed positive temperature. As the even periodic cubes grow, the symmetric zero-field magnetization converges in moments to a uniform direction with a deterministic positive magnitude. This magnitude equals the right derivative at zero field of the infinite-volume pressure. The law is expressed through self-adjoint linear combinations of the spin components and requires no joint measurement of noncommuting observables.
Spontaneous magnetization in the quantum Heisenberg ferromagnet
September 24, 2026 · source · cite as \cite{OAI:Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026}
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.
Result 271 · Mathematical physics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md