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SUMMARY:Reinforced Random Walk and a Supersymmetric Spin System on the Tre
 e - Peter Wildemann (Cambridge)
DTSTART:20240528T143000Z
DTEND:20240528T153000Z
UID:TALK217294@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Motivated by predictions about the Anderson transition\, we st
 udy two distinct but related models on regular tree graphs: The vertex-rei
 nforced jump process (VRJP)\, a random walk preferring to jump to previous
 ly visited sites\, and the H^{2|2}-model\, a lattice spin system whose spi
 ns take values in a supersymmetric extension of the hyperbolic plane. Both
  models undergo a phase transition\, and our work provides detailed inform
 ation about the supercritical phase up to the critical point: We show that
  their order parameter has an essential singularity as one approaches the 
 critical point\, in contrast to algebraic divergences typically expected f
 or statistical mechanics models. Moreover\, we identify a previously unexp
 ected multifractal intermediate regime in the supercritical phase. This ta
 lk is based on arxiv:2309.01221 and is joint work with Remy Poudevigne.\n
LOCATION:Venue to be confirmed
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