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The Ising Model and Phase Transitions, correlation length

Another important quantity is the correlation length, which is expected to be of the order of the lattice spacing for T is close to T_C . Because the spins become more and more correlated as T approaches T_C , the correlation length increases as we get closer to the critical temperature. The discontinuous behavior of the correlation \xi near T_C is \begin{equation} \xi(T) \sim \left|T_C-T\right|^{-\nu}. \tag{1} \end{equation}