Dynamical model of Ising spins

A two-dimensional dynamical model of Ising spins is introduced. Since we were not able to define energy in our system, we introduced an object called the disagreement function. This function controls the dynamics-minimizing it locally we decide upon spin flipping. Amazingly, local minimization of the disagreement function can lead to an increase of its global value. We present the phase diagram of the system and show that exactly the same initial conditions can lead the system to one of several, completely different final steady states.