• Corpus ID: 221139585

The Ising correlation $C(M,N)$ for $\nu=-k$

@article{Boukraa2020TheIC,
  title={The Ising correlation \$C(M,N)\$ for \$\nu=-k\$},
  author={Salah Boukraa and J-M Maillard and Barry M McCoy},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We present Painlev{e} 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 $\nu = -k$ where $\nu = \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$. 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… 

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