Abstract for the talk on 10.12.2020 (17:00 h)

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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12.12.2020, 02:31