Asymptotic formula for correlation decay in the stochastic model of planar rotators at high temperatures

We found the asymptotic formula for correlations decay $\langle f_A(x(0)),g_{A+k(t)}(x(t))\rangle$, when $t\to\infty$, $k(t)\to\infty$, $k(t)\in Z^d$, in the stochastic model of planar rotators on a lattice $x(t)=\bigl\{x_k(t),k\in Z^d\bigr\}$, $t\geq0$, $x_k(t)\in T^1$ at high temperatures. The basic methods we use are the spectral analysis of the Markov semigroup generator and the saddle-point method.