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SUMMARY:Triviality of the 4D Ising Model
DTSTART:20220518T120000Z
DTEND:20220518T140000Z
DTSTAMP:20241009T034100Z
UID:indico-event-7828@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Hugo Duminil-Copin (IHES)\n\nWe prove that the scali
ng limits of spin fluctuations in four-dimensional Ising-type models with
nearest-neighbor ferromagnetic interaction at or near the critical point a
re Gaussian. A similar statement is proven for the λφ4 fields over R^4 w
ith a lattice ultraviolet cutoff\, in the limit of infinite volume and van
ishing lattice spacing. The proofs are enabled by the models’ random cur
rent representation\, in which the correlation functions’ deviation from
Wick’s law is expressed in terms of intersection probabilities of rando
m currents with sources at distances that are large on the model’s latti
ce scale. Guided by the analogy with random walk intersection amplitudes\,
the analysis focuses on the improvement of the so-called tree diagram bou
nd by a logarithmic correction term\, which is derived here through multi-
scale analysis.\n\nhttps://indico.math.cnrs.fr/event/7828/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/7828/
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