Time-dependent correlation functions of the classical one-dimensionalXYmodel at infinite temperature

Abstract

Computer calculations of the time-dependent spin and energy correlation functions of the classical one-dimensional $\mathrm{XY}$ model at infinite temperature are reported. Plots of $〈S_z^i{S}_z^i\mathrm{}\left(t\right)\mathrm{}〉$, $〈S_z^i{S}_z^{i+1\mathrm{}}\mathrm{}\left(t\right)\mathrm{}〉$, $〈{\epsilon }^i{\epsilon }^i\mathrm{}\left(t\right)\mathrm{}〉$, and $\left(\frac{1}{2}\right)\left[〈S_x^i{S}_x^i\mathrm{}\right(t)\mathrm{}〉+〈S_y^i{S}_y^i\mathrm{}(t\left)\mathrm{}〉\right]$ out to times $Jt=9\mathrm{}$ are given (${\epsilon }^i$ is the energy-density operator and $\hslash J$ is the exchange integral). Comparison is made with the exact results for the spin-1/2 $\mathrm{XY}$ model. After an appropriate scaling of the exchange integral and normalization to the classical value at $t=0\mathrm{}$ the values of the spin-1/2 functions are close to the values of their classical counterparts for times up to $\mathrm{Jt}\approx 4$.