Zusammenfassung für den Vortrag am 10.12.2020 (17:00 Uhr)
Webinar “Analysis, Quantum Fields, and Probability”Michael Aizenman (Princeton University)
Marginal triviality of the scaling limits of 4D critical Ising and Phi^4 models
The talk will present the recent proof that in four
dimensions the spin fluctuations of Ising-type models at their critical
points are Gaussian in their scaling limits (infinite volume, vanishing
lattice spacing). Similar statement is proven for the scaling limits of
more general PHI^4 fields constructed through a lattice cutoff. The
proofs are facilitated by the systems’ random current representation, in
which the deviation from Wick's law are expressed in terms of
intersection probabilities of random currents with prescribed sources.
This approach previously yielded such statements for D>4. Their recent
extension to the marginal dimension was enabled by a multiscale analysis
of the critical clusters’ intersections. (Joint work with Hugo
Duminil-Copin.)
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