| A functional integration approach is developed to calculation of the correlation functions of spin operators in the XY Heisenberg chain. The peculiarity of the functional integrals is due to the fact that the integration variables are subject to the quasi-periodicity boundary conditions with respect of the imaginary time. Regularization by means of the generalized zeta-function is used. This allows us to obtain the answers in the form of the determinants of the matrix operators. The partition function and certain spin correlation functions are obtained. A time-dependent correlation function of the XX chain is considered, which plays a role of the generating function of random walks. Asymptotic behaviour of the correlation functions is considered. |
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