An efficient model for studying the dynamics of frustrated systems

We present a model based on determinist cellular automata architecture for studying systems with frustrated interactions that present elemental excitations, such as magnetic monopoles. This model is especially designed to be applied for systems with components that have energy levels much higher than $kT$. This would imply that for these systems thermal fluctuations are negligible and they can be analyzed under the supposition that the dynamic is produced at zero temperature. This category includes artificial magnetic spin ice systems and donor and recipient electrical charge molecular systems. The dynamics of these systems can be simulated in real time with this model, with a minimum of computational requirements. It can be an excellent complement to Monte Carlo methods and in some cases can even replace them directly. In this report, we show the designed structure and some interesting results obtained in studying the dynamics of emergent magnetic monopoles in artificial spin ice systems and excitations in graphane molecular arrays.