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SUMMARY:Marcin Lis (Faculty of Mathematics\, University of Vienna\, Austri
 a)
DTSTART:20200603T130000Z
DTEND:20200603T140000Z
DTSTAMP:20260423T024426Z
UID:PortMATHS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PortMATHS/2/
 ">On delocalization in the six-vertex model</a>\nby Marcin Lis (Faculty of
  Mathematics\, University of Vienna\, Austria) as part of Portsea Maths Re
 search Webinar\n\n\nAbstract\nWe show that the six-vertex model with param
 eter $c \\in [\\sqrt{3}\,2]$ on a square lattice torus has an ergodic infi
 nite-volume limit as the size of the torus grows to infinity. Moreover we 
 prove that for $ c \\in \\left[\\sqrt{2 + \\sqrt{2}}\, 2 \\right]$\, the a
 ssociated height function on $\\mathbb{Z}^2$ has unbounded variance.\nThe 
 proof relies on an extension of the Baxter–Kelland–Wu representation o
 f the six-vertex model to multi-point correlation functions of the associa
 ted spin model. Other crucial ingredients are the uniqueness and percolati
 on properties of the critical random cluster measure for $q \\in [1\, 4]$\
 , and recent results relating the decay of correlations in the spin model 
 with the delocalization of the height function.\n
LOCATION:https://researchseminars.org/talk/PortMATHS/2/
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