  We consider spin-$\frac{1}{2}$ model on the honeycomb lattice~\cite{Kitaev06}
in presence of a weak magnetic field $h_{\alpha }\ll 1$. Such a perturbation
destroys exact integrability of the model in terms of gapless fermions and
\textit{static} $Z_{2}$ fluxes. We show that it results in appearance of a
long-range tail in the irreducible dynamic spin correlation function: $%
\left\langle \left\langle s^{z}(t,r)s^{z}(0,0)\right\rangle \right\rangle
\propto h_{z}^{2}f(t,r)$, where $f(t,r)\propto \lbrack \max (t,r)]^{-4}$ is
proportional to the density polarization function of fermions.
