Computational Modeling of Spin Dynamics

The Ising model, originally developed in the 1920’s to analyse ferromagnetic properties has since found a myriad of other seemingly unrelated applications. An updated Ising model, Glauber’s spin dynamics, is used to examine phase changes in ferromagnetic materials and other systems. In the Glauber spin model, a system starts with some initial condition and over time the state of the undergoes small fluctuations that increase as more energy is put into the system. Then, there is a critical point where the system loses its initial condition and changes phase. Glauber’s spin model has been used to examine the changes that melt ponds in the arctic undergo over time. The model has been used in chemistry to determine whether polymer chains will form. Glauber’s model has even found uses in information theory. The goal of this project is to create an Ising model using Python then display some of the properties of the Ising model with a feedback mechanism coupling Glauber\u27s spin dynamics and the external forcing on the system. The one dimensional and two dimensional Ising models are examined. It is shown, as Ising did, that the one dimensional model does not predict any phase changes. It is also shown that the Glauber spin model does predict phase changes for a system