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SUMMARY:On the Supercritical Phase of the $\\phi^4$ Model
DTSTART:20250509T120000Z
DTEND:20250509T140000Z
DTSTAMP:20260504T201300Z
UID:indico-event-14254@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Franco Severo (Institut Camille Jordan\, Lyon 1)\n\n
 Probability and analysis informal seminar\nThe $\\phi^4$ model is a real-
 valued spin system with quartic potential. This model has deep connections
  with the classical Ising model\, and both are expected to belong to the s
 ame universality class. We construct a random cluster representation for $
 \\phi^4$\, analogous to that of the Ising model. For this percolation mode
 l\, we prove that local uniqueness of macroscopic cluster holds throughout
  the supercritical phase. The corresponding result for the Ising model was
  proved by Bodineau (2005) and serves as the crucial ingredient in renorma
 lization arguments used to study fine properties of the supercritical beha
 viour\, such as surface order large deviations\, the Wulff construction an
 d exponential decay of truncated correlations. The unboundedness of spins 
 in the $\\phi^4$ model imposes considerable difficulties when compared wi
 th the Ising model. This is particularly the case when handling boundary c
 onditions\, which we do by relying on the recently constructed random curr
 ent representation of the model.Joint work with Trishen Gunaratnam\, Chris
 toforos Panagiotis and Romain Panis.\n========\nPour être informé des pr
 ochains séminaires vous pouvez vous abonner à la liste de diffusion en 
 écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscrib
 e seminaire_mathematique PRENOM NOM"(indiquez vos propres prénom et nom) 
 et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/event/
 14254/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/14254/
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