Could be worse - Random topics in statistical physics, spin glasses, optimization and average case hardness
10 September 2025 | E. Malatesta
I’m a statistical physicist who has spent much of my time thinking about disordered systems, especially spin glasses and what they can teach us about learning and computation. Over the years I’ve found that the material I love requires patience to digest: ideas are spread across many books and papers, terminology shifts with time, and even paradigmatic toy models of learning and computation remain intricate when one tries to fully understand their landscapes, ground states, and dynamics.
This blog is an attempt to make that journey friendlier, at least in the way I like to approach it. I want to write slowly when slowness helps, be explicit about assumptions, and be transparent about what is rigorous, what is heuristic, and what still belongs to the folklore of the field. When several paths lead to the same conclusion, I will try to put them side by side, highlighting both their common ground and their differences. If a derivation hides a step, I will do my best to make it visible, while keeping the focus on the key conceptual ideas.
My interests are not confined to spin glasses so this blog is not just about that. The subject touches many other areas: statistical mechanics, algorithms and optimization, neuroscience, and more broadly computer science. I expect that my focus will evolve with time, so I cannot predict in advance what topics will appear here. Some posts will be short notes, others longer explorations, often with derivations or numerical simulations. I aim to make each entry self-contained, with links to earlier posts or external resources when needed. There will be no fixed roadmap: posts will appear as I find clarity.
If you are a physicist working on complex systems, a researcher from neighboring fields such as machine learning or optimization who is curious about the statistical-mechanics viewpoint, or simply a student who enjoys mathematics and physics, you may find something of interest here. My approach leans more toward the style of statistical physics than formal mathematics: I will often present short heuristic derivations that are not fully rigorous but that capture the essential ideas. When precise theorems exist, I will point to them, though I will rarely dwell on proofs. I strongly believe that non-rigorous arguments can still be valuable if they unveil new phenomena or shed light on results that were previously unexplained.
At the moment there is no possibility of interaction here: the site does not yet support comments in the way a typical blog would. I plan to add that feature in the future, so that feedback, questions, and corrections can flow in more naturally.