Lattice models of statistical physics

An important feature of non-quantum finite-dimensional lattice models is principal ability to get numerically exact solution on a set of finite-size lattices suitable for doing finite size scaling and thus get approximate solution of any infinite model.

Lattice gas and Ising model: Dynamic correlation function of Ising antiferromagnet

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.

Developing accurate analytical methods for disordered systems: Efficient perturbation expansion for disordered systems

It is an old idea that the perturbation series for the resolvent of a matrix can be rearranged so as to exclude the multiple scattering.