We consider the spin-1/2 model on the honeycomb lattice in the presence of a weak magnetic field hα << 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and static Z2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic spin correlation function: <<s(z)(t,r)s(z)(0,0)>> ∝ h(z)(2)f(t,r), where f(t,r) ∝ [max(t,r)]-4 is proportional to the density polarization function of fermions.