Kinetically Constrained A place to keep the longer thoughts of Doug Ashton.
Posts with the tag ising model:

The Renormalisation Group

A new video which more or less completes the critical phenomena series. Jump straight to it if you want to skip the background. One of my favourite topics is the critical point. I’ve posted many times on it, so to keep this short you can go back here for a summary. In brief, we’re looking at a small point on the phase diagram where two phases begin to look the same. The correlation length diverges and all hell breaks loose. Well, lots of things diverge. At the critical point all length scales are equivalent and, perhaps most remarkably, microscopic details become almost irrelevant.

Universality at the critical point

Time for more critical phenomena. Another critical intro I’ve talked about this a lot before so I will only very quickly go back over it. The phase transitions you’re probably used to are water boiling to steam or freezing to ice. Now water is, symmetrically, very different from ice. So to go from one to the other you need to start building an interface and then slowly grow your new phase (crystal growth). This is called a first order phase transition and it’s the only way to make ice. Now water and steam are, symmetrically, the same. At most pressures the transition still goes the same way – build an interface and grow.

Critical Point

I’m finally getting around to sharing what, for me, is the most beautiful piece of physics we have yet stumbled upon. This is the physics of the critical point. It doesn’t involve enormous particle accelerators and it’s introduction can border on the mundane. Once the consequences of critical behaviour are understood it becomes truly awe inspiring. First, to get everyone on the same page, I must start with the mundane - please stick with it, there’s a really cool movie at the bottom… Most people are quite familiar with the standard types of phase transition. Water freezes to ice, boils to water vapour and so on.