# Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?

Have the correlation functions of the XY spin chain model,

$$H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z$$

been calculated using a functional partition function with source terms?

By functional partition function I mean the partition function plus source terms (or generating functional) which allow correlation functions such as $\langle \sigma_l^x \sigma_{l+1}^x \rangle$ to be calculated analytically:

$$Z[\bar{\omega},\omega] = Tr \left[Exp \left[-\int_0^\beta d\tau H(a^{\dagger},a) - \int_0^\beta d\tau \sum_l (\bar{\omega} a + a^{\dagger} \omega) \right] \right]$$

where $H(a^{\dagger},a)$ is the XY Hamiltonian expressed in terms of spinless fermions (i.e. after a Jordan-Wigner transformation).

Edit: Anyone? An Ising chain would be fine too!

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