AI 中文总结
研究布卢姆 - 卡佩尔模型的李 - 杨性质，利用利布和索卡尔结果，发现虽因各向异性项在\(\beta \Delta> \ln 2\)时单自旋配分函数无李 - 杨性质，但铁磁相互作用能诱导出该性质，为相关研究提供新成果。
AI 中文摘要
李 - 杨理论基于1952年李政道和杨振宁证明的关于铁磁伊辛模型配分函数性质的定理，为理解各种自旋及类似模型中的相变和临界现象提供有力工具。有时该理论会应用于定理有效性未被证明的模型。利布和索卡尔的主要结果表明，对于给定铁磁模型，单自旋配分函数的相同性质可保证定理有效性。由于各向异性项，布卢姆 - 卡佩尔模型的单自旋配分函数在\(\beta \Delta> \ln 2\)时不具有李 - 杨性质。本文表明，即使在这些\(\beta \Delta\)值下，该模型中的铁磁相互作用也能诱导出李 - 杨性质，这是此类的首个结果。
英文摘要
The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by T. D. Lee and C. N. Yang in 1952. It provides powerful tools for understanding the very nature of phase transitions and critical phenomena in various spin and similar models. Sometimes, this theory is applied to models for which the theorem's validity has not been proved. By the main result of E. H. Lieb and A. D. Sokal, Commun. Math. Phys. 80, 153 (1981), for a given ferromagnetic model, this validity is guaranteed by the same property of the single-spin partition function. Due to the anisotropy term $\sum_i ΔS_i^2$, the single-spin partition function of the Blume-Capel model fails to have the Lee-Yang property for $βΔ> \ln 2$. In this article, we show that the ferromagnetic interaction in such a model can induce the Lee-Yang property, even for these values of $βΔ$. To the best of our knowledge, it is the first result of this kind.
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