  We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence
of weak magnetic field $h\ll J$. Such a perturbation treated in the second
order over $h$ leads to the power-law decay of irreducible spin correlation
function $S(\mathbf{r},t)=\left\langle \left\langle
s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto
h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max
(t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength
equal to 3 lattice constants. In the present Letter we sum main terms in all
orders of the perturbation theory for the correlation function
$S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in
terms of the effective low-energy Hamiltonian written in terms of Majorana
fermions, which in the presence of magnetic field acquire vector potential $A_x
\propto h_z^2$. Correspondingly, the wave vector of the oscillations in
$S(\mathbf{r},t)$ changes according to $\delta k \propto h_z^2$. We also
compute the dynamic structure factor $S(\mathbf{p},\omega)$; in the vicinity of
$\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads
as
$S(\mathbf{p},\omega)-S(\mathbf{p}_K,\omega)\propto\sqrt{\omega^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.
