How Do Magnets Work? An Introduction to the Ising Model

Why do magnets actually work? It turns out the answer lies in the collective coordination of trillions of microscopic objects. In this video, we will learn about one of the most important models in statistical physics: the Ising model. We explore how ferromagnetism arises from the interactions between "spins". But there is a catch: being too hot can shake these dipoles out of alignment, leading to a dramatic phase transition, just like a liquid turning into a gas. In the process, we will explore the philosophy of mathematical model building, learning how to reduce a complicated physical reality into a simpler model. Link to script: https://drive.google.com/file/d/1q-SH... ____________________________________ Timestamps: 0:00 - Introduction: What are Magnets? 02:18 - What is the Ising Model? 09:10 - Understanding Probabilities: The Boltzmann Distribution 17:37 - What is a Model Anyways? 18:57 - Solving the 1D Ising Model: The Method of Transfer Matrices 22:53 - Phase Transitions in the Ising Model 24:46 - Emergence 25:21 - The 2D Ising Model 26:49 - Why the 1D Ising Model has no Phase Transition 30:58 - Why the 2D Ising Model has a Phase Transition 32:51 - Concluding Thoughts ____________________________________ All animations were made with the Python library Manim ____________________________________ Background Music: Sleep Music No. 1 Chris Haugen