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Spin Glasses

Last update: 23 Sep 2025 22:40
First version: 6 May 2023

Yet Another Inadequate Placeholder

I am only being a little sarcastic when I say that a physicist interested in complex systems and trained in the 1990s (like me) was raised to look for spin glasses everywhere. There are times when I regard this as a childish thing I'm glad I put away, and times when it seems like a deep truth that the rest of the world would do well to appreciate...

Things I should already know the answer to: How does the Parisi et al.'s replica symmetry breaking relate to probabilists' ideas about graph limits? We've got this sequence of increasingly refined block-diagonal matrices, only every permutation of rows and columns is actually equally good, tending towards some sort of continuous limit function on the unit interval, so it seems like it ought to be a graphon, but maybe I'm missing something. For that matter, now that I start thinking about things in these terms, I am very puzzled about how overlap can be a physical order parameter... (Basically: any one sample from a mixture, no matter how large, can only tell you about that mixture component, not the distribution over mixtures.) --- I suspect that reading Talagrand would clear all this up for me, so I need to get around to doing so one of these decades.


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