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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-147@lptms.universite-paris-saclay.fr
DTSTART:20130527T143000Z
DTEND:20130527T160000Z
DTSTAMP:20130513T070512Z
URL:https://www.lptms.universite-paris-saclay.fr/seminars/seminaire-de-la-
 federation-phystat-sud-jesper-jacobsen/
SUMMARY:Séminaire de la Fédération PHYSTAT-SUD : Jesper Jacobsen - IPhT\
 , CEA-Saclay\, salle Itzykson - 27 Mai 13 14:30
DESCRIPTION:Critical manifolds for percolation and Potts models from graph 
 polynomials\nJesper Jacobsen (Labo. de Physique Théorique de l'Ecole Norm
 ale Supérieure\, Paris)\n \nThe first parameter to be fixed when studyin
 g a phase transition is the critical temperature. Somewhat surprisingly\, 
 this parameter is only known analytically for the simplest two-dimensional
  models (Ising model)\, or for more complicated models (Potts and O(n) vec
 tor models) on the simplest possible lattices. The known critical temperat
 ures are invariably given by simple algebraic curves. Some of these result
 s have very recently been proved mathematically by the technique of discre
 te holomorphicity.\nFor Potts and (bond or site) percolation models on any
  desired two-dimensional lattice we define a graph polynomial whose roots
  turn out to give very accurate approximations to the critical temperature
 s\, or even yield the exact result in the exactly solvable cases. This pol
 ynomial depends on a basis (unit cell) and its embedding into the infinite
  lattice. As the size of the basis is increased the approximation becomes 
 increasingly accurate. This\, on the one hand\, gives strong evidence that
  the critical temperature for the lattices with no known analytical soluti
 on may not be algebraic numbers\, and that conformal invariance will not h
 ave any counterpart in finite size (discrete holomorphicity). On the other
  hand\, the method determines the critical temperature to unprecedented ac
 curacy\, typically 12-13 significant digits for bond percolation threshold
 s. It also shows that the phase diagram of the Potts model in the antiferr
 omagnetic regime has an intricate and highly lattice-dependent structure.\
 n&nbsp\;\n&nbsp\;\n&nbsp\;
LOCATION:IPhT\, CEA-Saclay\, salle Itzykson\, CEA - Saclay\, Saclay\, Franc
 e
GEO:48.73668;2.180033999999978
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=CEA - Saclay\, Saclay\, Fra
 nce;X-APPLE-RADIUS=100;X-TITLE=IPhT\, CEA-Saclay\, salle Itzykson:geo:48.7
 3668,2.180033999999978
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