Kinetic Ising Model w/ Metropolis Algorithm скачать в хорошем качестве

Kinetic Ising Model w/ Metropolis Algorithm

This is a simulation of the kinetic Ising model. The kinetic Ising model is a way to dynamically update a system of binary states. This could be a system of quantized spins, a group of people who all have a yes or no opinion on something, voters who only have 2 candidates to choose from, etc. The only difference in these scenarios is the algorithm through which the states interact and update themselves. This simulation uses the Metropolis algorithm to evolve a system of up and down spins. The Metropolis algorithm treats this system as a Canonical ensemble (system at constant T that can exchange energy) and uses Boltzmann statistics to guide its evolution. This model is useful for explaining why things like iron can become spontaneously magnetized below the Curie temperature. Above the Curie temperate (T~2.269 in simulation), the spins point in random different directions due to thermal fluctuations. Once T decreases, it is energetically favorable for neighboring spins to align so domains/groups begin to form of both spins. Magnetism occurs because of spin alignment, so if the domains of one type begin to dominate the piece of iron is externally magnetic. In real iron, domains exist at room temperature but there are an equal amount of spin up and spin down domains. When an external magnetic field is applied, however, one direction is preferred so spins suddenly align and the iron becomes externally magnetic. This explains why one nail can pick up another nail when it is attached to a magnet. Without the magnet, the nail is internally magnetic (has domains) but externally non-magnetic (they cancel out). When a magnet is connected, one type of domain dominates and thus it becomes externally magnetic and acts just like the permanent magnet attached. This was only done on a 50x50 grid due to the limits of MatPlotLib, but with Taichi (a Python package) I can create a grid as large as my monitor resolution and have it compute directly on my GPU. It can also update the grid faster than MatPlotLib can even on this high resolution. The bitrate of the video is way too low to upload though which is why you see the MatPlotLib one.