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SUMMARY:Pinning and disorder relevance for the lattice Gaussian free field
  - Lacoin\, H (IMPA - Instituto Nacional de Matemtica Pura e Aplicada\, Ri
 o de Janeiro)
DTSTART:20150423T103000Z
DTEND:20150423T113000Z
UID:TALK59146@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Giambattista Giacomin (Universit Paris Diderot) \n\
 nWe present a rigorous study of the localization transition for a Gaussian
  free field on Zd interacting with a quenched disordered substrate that ac
 ts on the interface when the interface height is close to zero. The substr
 ate has the tendency to localize or repel the interface at different sites
  and one can show that a localization-delocalization transition takes plac
 e when varying the average pinning potential h: the free energy density is
  zero in the delocalized regime\, that is for h smaller than a threshold h
 c\, and it is positive for h>hc. For d=3 we compute hc and we show that th
 e transition happens at the same value as for the annealed model. However 
 we can show that the critical behavior of the quenched model differs from 
 the one of the annealed one. While the phase transition of the annealed mo
 del is of first order\, we show that the quenched free energy is bounded a
 bove by (h-hc)2+ times a positive constant and that\, for Gaussian disorde
 r\, the quadrat ic behavior is sharp. Therefore this provides an example i
 n which a { l relevant disorder critical exponent} can be made explicit: i
 n theoretical physics disorder is said to be { l relevant} when the disord
 er changes the critical behavior of a system and\, while there are cases i
 n which it is known that disorder is relevant\, the exact critical behavio
 r is typically unknown. For d=2 we are not able to decide whether the quen
 ched and annealed critical points coincide\, but we provide an upper bound
  for the difference between them. \n
LOCATION:Seminar Room 1\, Newton Institute
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