虚化学势下作为布洛赫函数的费米子与玻色子配分函数
Fermionic and bosonic partition functions at imaginary chemical potential as Bloch functions
AI总结：
该研究将有限温虚化学势下两类场论模型的相变映射为晶格变换，借助Clausen函数零点与极值，结合配分函数与布洛赫、万尼尔函数的对应，为研究相变及导体存在性提供新视角。
摘要：
我们指出，有限温度与虚化学势下d+1维Gross-Neveu模型与$CP^{N-1}$模型的相变，可映射为类Hubbard正六边形晶格到正方形晶格的变换，其中间步骤为特定的（不规则六边形类）曲面，这些曲面基于偶指标Bloch-Wigner-Ramakrishnan多重对数函数有序构造。Clausen函数$Cl_d(θ)$的零点与极值在分析中发挥重要作用：它们不仅让我们得以研究费米子与玻色子理论及其相变，还使我们能够探索导体存在的可能性——这一可能性源于两类模型的配分函数，与固态物理紧束缚近似中起关键作用的布洛赫函数和万尼尔函数之间的对应关系。
英文摘要：
We point out that the phase transitions of the $d+1$ Gross-Neveu and $CP^{N-1}$ models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen $Cl_d(θ) $ function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics.
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