Bloch定律的首个晶格修正
The first lattice correction to Bloch's law
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具体内容
稿件研究三维最近邻量子Heisenberg铁磁体，对每个固定自旋S=1/2,1,3/2,…证明Bloch定律的首个晶格修正。作者声称自发磁化亏损与完整理想磁振子密度相差o(β^{-5/2})，在主导Bloch项之外给出修正3ζ(5/2)(βS)^{-5/2}/(128π^{3/2})。磁化取热力学压强在零场处的右导数，先取体积极限再求场导数，最后取低温极限。
- 对每个固定自旋S=1/2,1,3/2,…证明Bloch定律的首个晶格修正
- 自发磁化亏损与理想磁振子密度相差o(β^{-5/2})，并给出显式修正项
- 磁化为零场处压强右导数，体积极限先于场导数，低温极限最后取
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英文原始摘要
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.
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