Spin glasses 4 scaled
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Magnetization of metal alloys and Machine Learning

Unveiling the properties of state-of-the-art computing techniques from a physics perspective

There is nothing new to be discovered in physics now. All that remains is more and more precise measurement. With these infamous words did renowned physicist Lord Kelvin sentence the end of physics back in the late 19th century. Thermodynamics and Electromagnetism were thought to be understood entirely, just as classical mechanics was from earlier years. Luckily, it would just take a couple of decades to discover the first quantum and relativistic theories, proving him wrong and opening new research areas.

Still, in our modern world, we usually tend to think that Lord Kelvin was, in some sense, correct, at least in what classical physics was concerned. “Of course, there is much research currently conducted in physics”, we say to ourselves, “but in the end, it is all modern, spooky physics. For sure, research in Physics will bring us cool quantum computing capabilities, help us understand tiny subatomic particles, and discover the wonders of dark matter, but still, every high school student knows that apples fall from trees and that compasses point towards the Earth’s magnetic pole”. And this way we prove, yet once again, that we humans are the only living creatures capable of tripping over the same stone twice. Because the truth is that there still is a lot of classical, ‘everyday’ physics that we do not understand. And by ‘everyday’ physics, I mean precisely that: phenomena that happen all around us every now and then and that, being so common to our everyday experience, should already be trivially and perfectly described and understood by scientists. Examples of those go from the more engineering-related topics, such as phase transitions of matter or fluid mechanics, to the more down-to-earth facts, such as rare weather events.

Our latest work: phase transition in spin glasses

In our recent work, we focused on studying one of such problems that might seem easy to the untrained eye: phase transitions. In particular, we concentrate on a kind of system called “spin glasses”. In lay terms, imagine that you have a collection of tiny magnets that can be pointing up or down (let us call them spins) that sit in a specific position within a particular structure or ‘lattice’. This lattice, which can be as complicated as one can imagine, is defined by some coils coupling spins together so that they can influence the state of others. These kinds of systems exhibit tremendously rich behaviors, which are very interesting from a physical standpoint. For example, they explain how a piece of iron gets magnetized when we put it into a magnetic field and, to put it into a broader context, the 2021’s Nobel Prize in physics was awarded to Giorgio Parisi for his contributions to the understanding of such systems.

However, the interest in this model is not just scientific, as current state-of-the-art technologies, such as some machine learning models, rely on the mathematical descriptions of these systems. Hence, the interest in the spin-glass intricacies is of a considerable size not only within the scientific community but also within the industrial one.

The problem with the Machine Learning version of these models is that they don’t resemble an ordinary physical magnet with all the atoms and interactions of the same type. Contrarily, the resulting ML model consists of spins interacting between them with coils of different lengths and strengths, as if someone had mixed many different materials and fused them together to form a single piece of metal. In this case, we don’t know how much magnetic field we need to magnetize this metal piece… in fact, we don’t even know if we can magnetize the piece at all, to begin with!

The question we addressed in this last work was then whether this magnetization (or phase transition) exists for various spin glass models. For that, we carried out simulations to explore the evolution of these systems for different temperatures, finally determining whether the system had undergone a phase transition or not. The results obtained in this work suggest that there indeed exists a phase transition in two-, three- and four-dimensional systems, which in some points contradict the common scientific belief. In this case, most scientific literature results point towards a phase transition in three and four dimensions but not in two. In comparison, we did get a transition in two dimensions as well. Which one is the correct answer? That cannot be stated until we obtain a general and strict proof, so further research is needed.

In the end, nevertheless, this is how research works; indeed, we are lucky enough to see that, again and probably for many years to come, Lord Kelvin was wrong. You can read the paper here.

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