Rigorous renormalization group and Ising criticality
The Ising model, a grid of tiny magnets that point up or down, has a sharp phase transition whose 3D critical exponents are known to many digits from computers, yet mathematicians cannot prove that they exist. The predicted behaviour of such models, and of random paths that never cross themselves, is proven mainly in four or more dimensions, where it is close to that of free fields.
Why it matters
A proof of scaling and universality in three and four dimensions would put the renormalization group, the main tool for phase transitions, on rigorous footing in the physical dimensions.
Review
H. Duminil-Copin, 100 years of the (critical) Ising model on the hypercubic lattice, arXiv, 2022. https://arxiv.org/abs/2208.00864 reference checked
Timestamp record
- Signed record
- 0b88a0ded9bd…
- Public log
- Entry 260, in checkpoint 2,123
- In the log by
- Block 969,698, 2026-10-03
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