Imagine a group chat with dozens of friends trying to pick a place to go on Friday night. One person wants to watch a movie, another insists on karaoke, a few only care that it’s affordable, and someone else wants good photos for social media. The more people join, the more tangled the conversation becomes. If you tried to “summarize” the whole chat with just one number that says how close everyone is to agreeing, it would feel a bit ridiculous. The situation is messy, with mini-groups, shifting alliances, and half-made plans. That, in a strange way, is close to what physicists face when they study certain messy materials called spin glasses, and it is precisely the kind of problem Parisi dives into.
Spin glasses are special kinds of magnets where tiny atomic “arrows” don’t all want to point in the same direction. Some pairs prefer to align, others prefer to oppose each other. Hence, the material ends up frustrated and disordered, more like your chaotic group chat than a neat row of soldiers. Earlier, scientists such as Edwards, Anderson, Sherrington, and Kirkpatrick attempted to describe this complex system with a single “order parameter,” essentially a single number that indicates the degree of order in the system. But when they pushed their formulas, they ran into absurd results, like predicting a negative entropy at very low temperature—roughly like saying a playlist has less than zero possible song orders. It was a sign that the description was too simple. Parisi’s key move is to show that, in a careful mathematical treatment called the replica approach, you don’t just need one parameter to describe a spin glass—you actually need an infinite number of them. Instead of one rating, you get a whole curve. This function indicates the similarity between different possible internal arrangements of the material.
Parisi builds this step by step. He starts with the old “one-number” picture, then lets the system be described by more and more parameters—first 1, then 3, then 5, and so on—constantly checking how the predicted energy and other properties behave near the critical temperature where the spin glass appears. With only a few parameters, the description already improves significantly, aligning well with more detailed calculations and computer simulations, and the previously observed negative entropy almost vanishes. As the number of parameters grows, the description approaches a limit where the internal structure of the spin glass is encoded in that function of one variable, defined between 0 and 1. In everyday terms, it’s like going from rating a movie with a single score out of 10 to having a whole profile: acting, soundtrack, story, cinematography, and then even more fine-grained sub-scores. The material is not captured by one label but by an entire landscape of overlapping “moods.”
The interesting part is what this hints at beyond the realm of physics. The function Parisi introduces contains all the information needed to compute physical quantities, such as how strongly the material responds to a magnetic field or how much energy it stores; however, its deeper meaning is still not fully clear in the paper. That uncertainty is a reminder that, in real life, too, complex systems—from your social circle to your mental health or even an online community—are rarely described well by a single number, such as a score, rank, or average. We often try anyway: GPA, follower count, likes, and a single “happiness” scale. Parisi’s work quietly suggests another attitude: when reality is messy and conflicted, expect it to need many parameters, perhaps even a whole continuous spectrum, to be described fairly. Instead of asking “What’s the one number that sums this up?”, we can ask “What is the shape of the whole picture?” Learning to think that way can make us more careful with statistics, more skeptical of oversimplified rankings, and more understanding of materials in a lab, and of people in our lives who, like spin glasses, don’t fit neatly into a single box.
Reference:
Parisi, G. (1979). Infinite Number of Order Parameters for Spin-Glasses. Physical Review Letters, 43(23), 1754–1756. https://doi.org/10.1103/PhysRevLett.43.1754
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