Sharif Digital Repository

Non-equilibrium systems refer to systems in which, unlike equilibrium systems, the initial condition plays an important role. Conventional methods in quantum field theory cannot be used to study these systems because they do not necessarily have a convergent perturbative expansion.In this thesis, we first briefly introduce the Ising model and fermions in the lattice gauge theory. We then introduce the two-particle irreducible (2PI) method as a tool to investigate nonequilibrium systems. Finally, using this method, we reformulate the Ising model for a system out of equilibrium