I am looking at McCoy's book about on Ising model because I am looking for the expectation value of two adjacent spins at the critical temperature in the infinite volume limit of the anisotropic Ising model.
He writes [Eq. 4.10(a) on p. 201] that at $T=T_c$ we have $\langle \sigma_{i,j} \sigma_{i+1,j}\rangle=\frac{2}{\pi}\text{coth}(2K_x)\text{gd}(2K_x)$ where $\text{gd}$ is the gudermannian function.
So in the Kadanoff-Ceva paper of 1971 it seams to me that it is written that it is implicitly that the expectation value of two horizontal adjacent spins is $\text{tanh}(2 K_x)$ to ensure that the expectation value of the energy field is zero.
Can someone confirm which of the results is true?
Further McCoy writes that the expectation value of next-nearest spins $\langle \sigma_{i,j} \sigma_{i+1,j+1}\rangle=2/\pi$. Is there some intuition that this is true? I guessed that this value should depend on the coupling constants.