What you see in the upper panel is a 500×500 lattice. Each space (we call them spins) is in one of two states: either orangered or periwinkle. You can imagine this as an array of little elementary magnets, that can either be aligned parallel or antiparallel to each other.

The orientation of each spin is determined by two contributers:

1. Neighbor interaction: Neighboring spins prefer to be in the same state. E.g. if one spin is orangered, its neighbors have an increased likelihood of also being orangered. The same goes for periwinkle spins.

2. Temperature: It acts a a ‘random force’ which causes disorder. Temperature doesn’t care about neighbors, it randomly flips spins around.

We start at low temperatures. Thus neighbor interactions dominate and the lattice is fully magnetized (all orangered). As the temperature increases, its influence on the system becomes more important. The correlation between neighbors decreases and at the end of the gif, temperature effects dominate over neighbor interactions. Thus at the end, spins are aligned randomly.

The magnetization plot in the bottom panel simply measures the balance of orangered vs. periwinkle. Magnetization = 1 means fully magnetized, e.g. all orangered. Magnetization = 0 means an equal share of orangered vs. periwinkle. This is the demagnetized state, as all elementary magnets cancel each other out on larger length scales.

Making off:

Metropolis Monte-Carlo algorithm. Implementation and visualization in Python.

What you see in the upper panel is a 500×500 lattice. Each space (we call them spins) is in one of two states: either orangered or periwinkle. You can imagine this as an array of little elementary magnets, that can either be aligned parallel or antiparallel to each other.

The orientation of each spin is determined by two contributers:

1. Neighbor interaction: Neighboring spins prefer to be in the same state. E.g. if one spin is orangered, its neighbors have an increased likelihood of also being orangered. The same goes for periwinkle spins.

2. Temperature: It acts a a ‘random force’ which causes disorder. Temperature doesn’t care about neighbors, it randomly flips spins around.

We start at low temperatures. Thus neighbor interactions dominate and the lattice is fully magnetized (all orangered). As the temperature increases, its influence on the system becomes more important. The correlation between neighbors decreases and at the end of the gif, temperature effects dominate over neighbor interactions. Thus at the end, spins are aligned randomly.

The magnetization plot in the bottom panel simply measures the balance of orangered vs. periwinkle. Magnetization = 1 means fully magnetized, e.g. all orangered. Magnetization = 0 means an equal share of orangered vs. periwinkle. This is the demagnetized state, as all elementary magnets cancel each other out on larger length scales.

Making off:

Metropolis Monte-Carlo algorithm. Implementation and visualization in Python.

This is actually kinda neat.