Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth 
Date  Jeudi 19 Mai 2022 
Heure  11:00 
Institut  LPTHE 
Salle  LPTHE library 
Nom de l'orateur  DuminilCopin 
Prenom de l'orateur  Hugo 
Addresse email de l'orateur  
Institution de l'orateur  IHES 
Titre  Marginal triviality of the scaling limits of critical 4D Ising and ϕ_4^4 models 
Résumé  In this talk, we will discuss the scaling limits of spin fluctuations in fourdimensional Isingtype models with nearestneighbor ferromagnetic interaction at or near the critical point are Gaussian and its implications from the point of view of Euclidean Field Theory. Similar statements will be proven for the λϕ4 fields over R^4 with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing. The proofs are enabled by the models' random current representation, in which the correlation functions' deviation from Wick's law is expressed in terms of intersection probabilities of random currents with sources at distances which are large on the model's lattice scale. Guided by the analogy with random walk intersection amplitudes, the analysis focuses on the improvement of the socalled tree diagram bound by a logarithmic correction term, which is derived here through multiscale analysis. 
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