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SUMMARY:Phase transitions of the graphical representations of the Ising mo
 del  - Frederik Ravn Klausen (University of Copenhagen) 
DTSTART:20231107T140000Z
DTEND:20231107T150000Z
UID:TALK208189@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:After much success in using the double random current represen
 tation in the study of the Ising model\, Duminil-Copin posed the question 
 in 2016 of determining the (percolative) phase transition of the single ra
 ndom current. By relating the single random current to the loop O(1) model
 \, we prove polynomial lower bounds for path probabilities (and infinite e
 xpectation of cluster sizes) for both the single random current and loop O
 (1) model corresponding to any supercritical Ising model on the hypercubic
  lattice. Thereby partially resolving the posed question. \n\nIn this talk
 \, I will gently introduce graphical representations of the Ising model an
 d their relations through the uniform even subgraph. Afterward\, we discus
 s new results whose surprising proof takes inspiration from the toric code
  in quantum theory.\n\nBased on joint work with Ulrik Tinggaard Hansen and
  Boris Kjær: https://arxiv.org/abs/2306.05130.
LOCATION:MR12
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