In the realm of physics, Ising model has been and probably will be an useful model for our intuition. Naively speaking, our world is full of local interactions yet the consequences are very likely to be long range through long range correlations. The famous Ising model is a key model of such concepts.

Ising model deals with a system of spins and their interactions. To build up the dynamics of a system, we need the configuration of it as well as the interactions. In Ising mode, a bunch of spins are described by , where could be scalars that take discrete values or vectors phenomenologically. For simplicity we take the path of discretized values, . The interactions are two body interactions is related to the descriptioin of energy

where indicates the strength of the interactions between the two spins.