Conformal invariance and \(2D\) statistical physics. (English) Zbl 1154.82009
Summary: A number of two-dimensional models in statistical physics are conjectured to have scaling limits at criticality that are in some sense conformally invariant. In the last ten years, the rigorous understanding of such limits has increased significantly. I give an introduction to the models and one of the major new mathematical structures, the Schramm-Loewner Evolution (\(SLE\)).
MSC:
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
| 30C35 | General theory of conformal mappings |
| 60J65 | Brownian motion |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
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