The Renormalisation Group
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it as a ready-made picture of coarse-graining, scale invariance and fractal behaviour near the Ising critical point when discussing the renormalisation group.
Recommended by 0 people across 0 different months, 2020 to 2022.
What it is
A one-minute silent visualisation of renormalisation group flow in the 2D Ising model. Three huge configurations (2^34 spins each) near the critical point are repeatedly coarse-grained, and the ones slightly off criticality flow away to the ordered or disordered fixed-point phases while the critical one stays self-similar. It is made by Douglas Ashton and released under Creative Commons.
What people said
Cites Bertram · 2020-05 · Physics Stack Exchange · on “Finding the critical temperature in the zero field Ising model via renormalisation”
Inspired by images such as these [this video] , I would think that one can find the critical temperature in the zero-field Ising model computationally as follows: Start with any initial temperature $T$ and calculate the magnetisation $M_0$ , Coarse grain in blocks and calculate the magnetisation at this level $M_1$ , If $|M_1|>|M_0|$ , $T<T_c$ , otherwise $T>T_c$ , Choose a new value of $T$ closer to $T_c$ and run the model again, Repeat the procedure until $|\Delta M|<\epsilon$ , with $\epsilon$ small. However, as this is far simpler than the Monte Carlo methods I have looked at, I suspect that this will not work. If my suspicion is correct, what am I missing?
Cites Kai · 2022-02 · Physics Stack Exchange · on “I'm missing the point of renormalization in QFT”
Here's some complementary perspective to the excellent answer by AccidentalFourierTransform. This turned out very long, but this is a huge topic which can't be entirely summarized in one answer. An important point I want to make is that renormalization is conceptually independent of either the quantum nature of QFT or the field theory nature of QFT, and is rather a ubiquitous and foundational concept that really gets to the core of many-body physics (i.e. physics of many interacting degrees of freedom). QFT just so happens to be the "ultimate" many-body problem (infinitely many interacting quantum harmonic oscillators filling spacetime) Renormalization and Coarse-Graining The original cleare
Cites Lau Jack · 2022-10 · Physics Stack Exchange · on “Under dynamic scaling, Ising model emerge fractals, which implicate what？”
In the lecture note of statistic field theory of David Tong, Fluctuations occur on all length scales, big and small. he post a link, a youtube video, which describe the Ising model in different scale, especially in Tc, and display the fractal behavior. So, I want to know does the fractal & chaos have some relationship with many-body physics? On the one hand, can we use the tools of chaos to describe strong-correlation physics? On the other hand, could we use semi-classical chaos theory to describe phase transition? Thanks in advance! enter the YouTube video here [this video]