Douglas Ashton


Scale Invariance.

For a longer introduction see the Blog Post..

At the critical point we lose a sense of scale and our system begins to look the same on every length scale. Here is an example of a critical Ising model made of 17 billion lattice sites. The video shows snapshots at different zoom levels but it becomes impossible to tell which one is which.

All videos are available in full HD and look good full screen.


Universality.

For a longer introduction see the Blog Post..

A consequence of losing a sense of scale is that we also lose the details of the microscopic interactions. Only broad features such as symmetry, long/short range interactions seem to be important putting different systems into broad universality classes. This video shows a Lennard-Jones fluid alongside an Ising model both at their critical points. If you zoom out enough then you can't tell which one is which.


The Renormalisation Group.

For a longer introduction see the Blog Post..

This zooming out process connects well with the idea of a renormalisation "flow". Starting with three systems close to the critical point. All three look like the snapshots have the same temperature. We gradually zoom out and plot what the temperature looks like. Above and below the critical point as you zoom out you flow to fixed points of a paramagnet and a ferromagnet respecitively. Exactly on the critical point you can zoom out forever and not flow away.