# Lattice gas and Ising model

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.

## Results

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.

## Publications

- Dynamic correlations in an ordered c(2×2) lattice gas, Seminar talk at Institute of Physics, Kiev (2006) – pdf, pdf in ukrainian
- P. Argyrakis, M. Maragakis, O. Chumak, A. Zhugayevych, Dynamic correlations in an ordered c(2×2) lattice gas, Phys. Rev. B 74, 035418 (2006) – arXiv:0709.1623