Spin-correlation functions of the anisotropic XY chain

We have calculated the spin-correlation functions (in the x, y, and z directions) in the linear spin-(1/2 XY system for both isotropic and anisotropic couplings. The study of zero-temperature correlation functions shows that a long-range order develops in the direction in which the coupling is stronger, but no such ordering exists for isotropic systems. We have studied the temperature variation of inverse correlation lengths in these directions and it has been found that at T=0 all the correlation lengths (ξ_x, ξ_y, ξ_z) diverge in the isotropic case. On the other hand, in the anisotropic case, the correlation length diverges in the direction (either x or y) in which the coupling becomes stronger. The results are compared with the experimental data on Cs₂CoCl₄. The critical exponents (η’,ν’) of the correlation function and correlation length are also calculated near the critical temperature (T=0) for different anisotropies, and it is found that the system behaves like an Ising model when a little anisotropy is introduced.