Many dynamic properties of a lattice system is encoded in its equilibrium two-point two-time correlation function. Its calculation is nontrivial in contrast to the static case for which various series methods exist. In particular, the BBGKY approach developed for a classical gas is not directly transferable to a lattice gas because the equation for one-particle distribution function involves not only two-particle but also higher order distribution functions. Yet the analysis of the snapshots shows that aside from the critical point the system can be viewed as a gas of weekly interacting structural defects complicated by the presence of transient configurations.
In our paper we extend the low-temperature expansion method to include the time-dependence and the transient configurations. The obtained correlation function is accurate within few percent for the temperatures up to 0.7 of the critical temperature.