The actual physics part is kind of boring, so I'm gonna spoiler it and post the cool pictures.
(https://i.imgur.com/hh2s4Phl.png)
High Temperature
(https://i.imgur.com/9CBavZD.png)
Low Temperature
(https://i.imgur.com/eyVKUwZ.png)
Vortices Highlighted
An initially random state cooling down.