论文标题
$ c（m，n）$ for $ν= -k $
The Ising correlation $C(M,N)$ for $ν=-k$
论文作者
论文摘要
我们向普通伊斯（Painlev {é} vi sigma形式的方程式介绍了一般的低温和高温两点相关函数$ c（m，n）$，在特殊情况下，$ m \ m \ m \ leq n $在特殊情况下$ c $ν= -k $ where $ν= \，\ sinh 2e_h 2e_h/k_bt/k_bt/k__bt/\ sinh 2eh 2eh 2e_v/kbt $。更具体地说，根据两个整数$ m $和$ n $出现的四种不同的非线性ODE：这四种非线性ODE分别对应于分别区分低和高温，以及$ m+n $偶数或奇数。当$ν= -1/k $时，这四个不同的非线性ODE也适用于$ m \ ge n $。对于低温行相关函数$ c（0，n）$带$ n $奇数，我们再次为此选择的$ν= \，-k $条件展示，这是PainlevéVisigma函数的一个了不起的现象，是四个Painlevévivi vi sigma函数的总和，具有相同的okamoto parameters。我们在此$ν= \，-k $ case中显示$ t <t_c $，还有$ t> t_c $，$ c（m，n）$，$ m \ leq n $作为$ n \ times n $ n $ toeplitz clastigant。
We present Painlev{é} VI sigma form equations for the general Ising low and high temperature two-point correlation functions $ C(M,N)$ with $M \leq N $ in the special case $ν= -k$ where $ν= \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$. More specifically four different non-linear ODEs depending explicitly on the two integers $M $ and $N$ emerge: these four non-linear ODEs correspond to distinguish respectively low and high temperature, together with $ M+N$ even or odd. These four different non-linear ODEs are also valid for $M \ge N$ when $ ν= -1/k$. For the low-temperature row correlation functions $ C(0,N)$ with $ N$ odd, we exhibit again for this selected $ν= \, -k$ condition, a remarkable phenomenon of a Painlevé VI sigma function being the sum of four Painlevé VI sigma functions having the same Okamoto parameters. We show in this $ν= \, -k$ case for $ T < T_c $ and also $ T > T_c$, that $ C(M,N)$ with $ M \leq N $ is given as an $ N \times N$ Toeplitz determinant.
