论文标题
Ising相关函数C（M，N）的lambda扩展
The lambda extensions of the Ising correlation functions C(M, N)
论文作者
论文摘要
我们以教学的启发式动机重新审视，二维ISING模型的低温行相关函数C（M，N）的Lambda扩展。特别是，使用这些单参数系列来理解$λ$的选定值的变形理论，即使用M和N整数使用$λ= \ cos（π\，m/n）$，我们表明这些系列产生了扰动系数，是d-finite功能的普遍化形式。作为副产品，这些精确的结果在第一和第二类的完整椭圆积分上提供了无限数量的高度非平凡的身份。这些结果强调了Jacobi Theta函数和Jacobi形式的基本作用，当根据椭圆机功能的Nome重写时，先前的D-FINITE函数是Jacobi Theta函数的（相对简单）合理的功能。
We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions C(M,N) of the two-dimensional Ising model. In particular, using these one-parameter series to understand the deformation theory around selected values of $λ$, namely $λ= \cos(π\, m/n)$ with m and n integers, we show that these series yield perturbation coefficients, generalizing form factors, that are D-finite functions. As a by-product these exact results provide an infinite number of highly non-trivial identities on the complete elliptic integrals of the first and second kind. These results underline the fundamental role of Jacobi theta functions and Jacobi forms, the previous D-finite functions being (relatively simple) rational functions of Jacobi theta functions, when rewritten in terms of the nome of elliptic functions.
