Date of Original Version
The dynamics of the classical X X Z model with uniform interaction is nonlinear for N≥2 spins and nonintegrable for N≥3. However, the nonlinearities disappear in the thermodynamic limit N→∞, and the spin autocorrelation functions can be determined exactly for infinite temperature. The function 〈S z i (t)S z i 〉 exhibits a Gaussian decay to a nonzero constant, and the function 〈S x i (t)S x i 〉 decays algebraically to zero or like a Gaussian, depending on the type (easy axis or easy plane) and amount of uniaxial anisotropy.
Jian-Min Liu, and Gerhard Müller. The classical equivalent-neighbor XXZ model: exact results for dynamic correlation functions. J. Appl. Phys. 67 (1990), 5489-5491.
Available at: http://dx.doi.org/10.1063/1.345860