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In the XY Ising model we have the following Hamiltonian:

$$H=-J\sum_i \cos(\theta_i-\theta_{i+1}).$$

From this I found that $\langle \theta_i| T | \theta_{i+1}\rangle = \exp(\beta J \cos(\theta_i-\theta_{i+1})$. I really have no clue how to find the eigenfunctions and eigenvalues in this case. Any hint will be appreciated.

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