Statistical Mechanics of the $\mathrm{XY}$ Model. IV. Time-Dependent Spin-Correlation Functions

We compute the correlation functions $〈S_0^x\mathrm{}\left(t\right)\mathrm{}{S}_R^x\mathrm{}\left(0\right)\mathrm{}〉$ and $〈S_0^y\mathrm{}\left(t\right)\mathrm{}{S}_R^y\mathrm{}\left(0\right)\mathrm{}〉$ at $T=0\mathrm{}$ for the one-dimensional $\mathrm{XY}$ model in the presence of a magnetic field.