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Phys-47-A1 · revision r1 · on Phys-47

OpenAI claim summary for Phys-47

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status: open. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

For the nearest-neighbor model, magnetization deficit is claimed equal to ideal-magnon density up to $o(\beta^{-5/2})$, including the stated $\zeta(5/2)$ lattice correction. The question retains these same parameters and conventions. Within these assumptions, this is a claimed affirmative answer to the stated question.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. The first lattice correction to quantum Bloch magnetization
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Result 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

The first lattice correction to quantum Bloch magnetization

OpenAI's claim

OpenAI presents a proof in the selected manuscript. For the nearest-neighbor model, magnetization deficit is claimed equal to ideal-magnon density up to $o(\beta^{-5/2})$, including the stated $\zeta(5/2)$ lattice correction.

Mathematical statement of the claimed result

Result 1.
For the three-dimensional coupling-one nearest-neighbor spin-$S$ quantum ferromagnet, define spontaneous magnetization $m_S(\beta)$ by the thermodynamic pressure's right field derivative at zero. Put \[ \varepsilon_S(k)=2S\sum_{j=1}^3(1-\cos k_j),\qquad n_S^{\mathrm{sw}}(\beta)=\int_{[-\pi,\pi]^3} \frac{d^3k}{(2\pi)^3(e^{\beta\varepsilon_S(k)}-1)}. \] For each fixed $S\in\{1/2,1,3/2,\ldots\}$, the assertion is \[ \lim_{\beta\to\infty}(\beta S)^{5/2} [S-m_S(\beta)-n_S^{\mathrm{sw}}(\beta)]=0. \] Thus the full lattice spin-wave integral captures the magnetization deficit through the stated scale.

Outline of the argument

Capacity comparison controls pinned return cycles on a period. Sparse-obstacle propagation and an ideal-potential profile identify comparison sources whose cancellation improves the error beyond the leading Bloch term, allowing the next dispersion coefficient to survive.

Formal verification

For family 271, the selected theorem constructs low-temperature zero-field magnetized KMS states for all dimensions at least three and all positive spins. The Bloch expansion, lattice correction, and spherical moment law are separate unselected companions. No Comparator is assigned to the selected manuscript here; the family page selects other papers or supporting statements. This site has not executed the Lean code. The scope descriptions do not certify the remaining manuscript arguments.

Status caveat

OpenAI attributes these manuscripts to work by an internal model. Its release cautions that arguments without formalization can contain mistakes. This catalogue has not independently checked the proofs; the labels report the mathematical claims attributed to OpenAI.

Sources