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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Conformal invariance of boundary touching loops of
FK Ising model - Kemppainen\, A (University of He
lsinki)
DTSTART;TZID=Europe/London:20150127T150000
DTEND;TZID=Europe/London:20150127T160000
UID:TALK57529AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57529
DESCRIPTION:Co-author: Stanislav Smirnov (University of Geneva
and St. Petersburg State University) \n\nI will p
resent a result showing the full conformal invaria
nce of Fortuin-Kasteleyn representation of Ising m
odel (FK Ising model) at criticality. The collecti
on of all the interfaces\, which in a planar model
are closed loops\, in the FK Ising model at criti
cality defined on a lattice approximation of a pla
nar domain is shown to converge to a conformally i
nvariant scaling limit as the mesh size is decreas
ed. More specifically\, the scaling limit can be d
escribed using a branching SLE(?\,?-6) with ?=16/3
\, a variant of Oded Schramm's SLE curves. We cons
ider the exploration tree of the loop collection a
nd the main step of the proof is to find a discret
e holomorphic observable which is a martingale for
the branch of the exploration tree. \n\nThis is a
joint work with Stanislav Smirnov (University of
Geneva and St. Petersburg State University)\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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