Abstract
We calculate the spin-spin correlations and the magnetic susceptibility of the quantum one- and two-dimensional $\mathrm{XY}$ models with $S=1,$ using the two-time Green's function method and performing a decoupling proposed by Kondo and Yamaji for cases with no long-range order. A set of self-consistent equations of the correlation functions are derived and solved numerically. We present results for the correlation functions, susceptibilities, and specific heat for the whole range of temperature.
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