Transcription
Watch this. What just happened? The answer to that question explains how water turns to vapor, how opinions spread on social media, how neurons fire in the brain, how to make the best cup of coffee, and why fluids do this. What's the connection between all of these things?
First things first, what just happened here? This is a piece of steel that contains iron. Iron behaves as a temporary magnet at room temperatures. What makes it magnetic is the orientation of its individual atoms. Each atom has its own magnetization which we call a dipole. In the presence of a magnetic field, the dipoles align with the magnetic field, making the iron magnetic. The magnetization of the entire piece of steel is the combined average magnetization of all of its atomic dipoles.
But something interesting happens when we heat it up. At a threshold temperature called the Curie temperature, it suddenly loses its magnetization, or in physics talk, it undergoes a sudden transition from a magnetic phase to a non-magnetic phase. If we plot how the magnetization behaves when temperature increases, we get a graph that looks like this. You can see this sudden drop-off of magnetization. This is called a phase transition.
What characterizes a phase transition is a sudden, dramatic change in the state of something, like from a liquid to a gas. Laminar flow to turbulent flow. And in this case, a magnet going from a magnetic state to a non-magnetic state. This is a bit weird when you think about it. Most physical phenomena go through a gradual change. Why this sudden transition? And why should a magnet lose its magnetization at all?
In 1920, the physicist Will Helm lens wondered about the mystery of magnetization as well. To avoid dealing with the messiness and complexity of all the atoms in a magnet, he developed a simplified model, now called the Ising model. He hoped that by studying the simplified model, he could understand the behavior of a real magnet. He imagined a magnet as a grid of dipoles. Each dipole could point either up or down. Just like in a real magnet, if the majority of dipoles are pointing up, the magnetization of the whole system is up. And if the majority of dipoles are pointing down, the magnetization of the whole system is down.
Each dipole produces its own local magnetic field which can influence its neighbors. Neighboring aligned dipoles have lower energy, whereas neighboring anti-aligned dipoles have higher energy. The total energy of the system is determined by the total alignments of all the dipoles. But why do we care about the system's energy?
Well, let's get back to a basic principle in physics. In many physical systems, objects want to go from high energy to low energy. Think of a ball falling from some height to the ground. The ball has a lot of potential energy when it's up high, but it naturally wants to move to a more stable, lower energy state. Similarly, in physics, systems tend to rearrange themselves to minimize their energy. The same goes here. The configurations we'll most likely see are the ones that have the lowest energies. In other words, the lowest energy states are the most probable. We can say that the system wants to minimize its energy. At absolute zero, the most probable states are the all up and all down configurations.
But what happens when we increase temperature? Well, there's another physical rule at play: the second law of thermodynamics. Systems in nature tend to move toward more disorder over time, or in physics talk, they maximize their entropy. Just think about how perfume molecules spread out over the whole room, mixing with the air molecules. They don't just stay neatly ordered in one corner, or how milk molecules naturally mix with the tea molecules. In the same way, the system of dipoles wants to maximize its entropy.
So, we have two opposing forces, a tug-of-war between energy minimization and entropy maximization. At low temperatures, energy minimization dominates and most of the dipoles are aligned with each other. There isn't enough thermal energy to jiggle the dipoles. The whole system has a net direction. So magnetization is observed. But when we increase the temperature, it gets so hot that the interaction energies between dipoles are minuscule compared to the amount of thermal energy. The dipoles fluctuate wildly, causing their directions to cancel out, and the system loses its magnetization.
So far, the Ising model is doing a great job of modeling a real-life magnet. At low temperatures, it's magnetic, and at high temperatures, it loses its magnetization. So, does it predict this abrupt phase transition as well? It turns out the answer is yes. This is a simulation of the Ising model at different temperatures. You can see that around this temperature, the system changes very abruptly. I'll play that again so you can see it again. Right here. Why? You can probably guess that this is the Curie temperature, otherwise known as the critical temperature. And something very interesting happens right at the critical temperature.