Renormalization: Why Bigger is Simpler

A submission to #SoME2.
A short introduction to renormalization techniques as they appear in statistical physics, aiming to simplify the mathematics as much as possible. The goal is to explain why matter becomes simpler as you zoom out from the microscopic, and how this leads naturally to phase transitions. Text version to follow.

This is a reupload with a couple typos fixed.

00:00 Introduction
02:13 States and probabilities
03:16 The Gibbs distribution
03:56 Course-graining
05:05 Hamiltonians
06:30 Renormalization calculation
07:38 Details of calculation
09:45 Renormalized coefficients
10:44 Renormalization flow
12:18 Fixed points
13:30 Particle physics
14:09 Phase transitions
15:42 Summary
16:19 Closing

[josefreire]

Excellent, lkkely the best introduction to RG in the Internet.

[pecan]

It's rare that I find a video that somehow just makes the world make more sense but this is such an insightful explanation for a formerly seemingly magical phenomenon (phase transitions).

[pacificll]

You cannot imagine how much this video (the original) has been important for me, it sparked so much new understanding and interest! Thank you so much and I would love to see more of your videos!

[pdelong]

Thanks for the explanation. I came to the idea of renormalization by way of particle physics, and the concept was a mystery to me for decades. This video helped to start to dispel some of that mystery (though I'd have to look more closely at the math and play with it myself, to really understand it).

And as a bonus, you also explained the shape of phase transition diagrams, which is something from chemistry class that always bugged me, with its seeming arbirariness.

[skywalker]

Much thanks, it's really rare to find clear explanations about this subject !

[GermanTutorials]

Wow i really didn't thought that renormalization can be visualized that beautifully and enlightening when i learned in. You really nailed it! Please make more videos of advanced topics like that!

[cstockman]

Bravo, a wonderful explanation. After trying for years to understand renormalization, this video has bridged the gap in my brain

[NeverEver]

Although I am not a fan of this idea of emergence I have to thank you for the explanation. It is much better to understand and to the point than on the big channels ❤

[宝宝-nq]

Wow, this video is amazing! It just cleared up so many questions I’ve been struggling with for a while.

[WonkaWastelander]

Amazing explanation!! Standing ovation for you good sir!

[cheedozer]

This was a really great way to show the essence of renormalization! Nice and easy to digest, while still inspiring further investigation.

[jacobvandijk]

@ 6:28 Makes me think of a Quartic Interaction (without the KE-term) in particle physics: with a and b as the coupling-constants, and m as the field.

[AbsolutelyNoOne]

Very few videos have blown my mind like this

[jensphiliphohmann]

Thank you for the vid. I'll have to rewatch it, of course, maybe even several times, but this makes some things clear which I kind of already knew due to lectures in statistical mechanics.
BTW it explains how we can be pretty sure about the large scale fate of our universe in some 10¹⁰⁰ years while not being able to even predict the wheather on Earth in precisely 4 months.

[michaelblankenau]

Excellent . Must be fun to be a genius and understand this like you do .

[magicponyrides]

Hot damn, this really felt like an epiphany to me. Great job.

[AlexandreMelanson]

Very nice introduction, thanks. Would you have any references to suggest where we might learn more on this topic?

[onlyeyeno]

Thanks for a fantastic video
As the ignoramus that I am I cant claim that I followed the maths fully. But despite this I felt that I could grasp the gist of the main principles! Which says a lot about the quality of the video imho :)
Best regards

[williamdavis]

Great video! Any recommendations for books on this topic?

[oldcowbb]

seeing the phase plot makes my control theory ass so excited, maybe we can establish some Lyapunov stability of a renormalization fix point. I don't know if it is useful or not