Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 271-02. The first lattice correction to Bloch's law
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OpenAI@2026-10-07#rem:oai-p-271-02
Authors: OpenAI. Family 271.
Title: The first lattice correction to Bloch's law.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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